ARCHIVES OF ECONOMIC HISTORY Volume ÃV No 2 July - December 2003
APXEION OIKONOMIKH™ I™TOPIA™ TfiÌÔ˜ XV T‡¯Ô˜ 2 πÔ‡ÏÈÔ˜ - ¢ÂΤ̂ÚÈÔ˜ 2003
CONTENTS - ¶EPIEXOMENA
§.£. Ã√Àª∞¡π¢∏™: ¶ÂÚ› ÙÔ˘ ‰ÈÏÔÁÚ·ÊÈÎÔ‡ Û‡ÛÙËÌ·ÙÔ˜ ÂȘ ÙÔ µ˘˙¿ÓÙÈÔÓ (On the double - entry system during byzantine times) ...... 5 AUKE R. LEEN: Uncertainly, taxation and entrepreneurial entry ...... 17 G. HALKOS - I. S. KEVORK: Confidence intervals in stationary autocorrelated time series ...... 31 G. A. VAMVOUKAS: An Empirical Analysis of the Marshall - Lerner Condition . . . . . 53 G. E. SKOULAS: Syndicalism and Education in the Age of Globalization and Information ...... 63 N. SYKIANAKIS: Factors affecting Greek FDIs in the Balkans: The case of the ice cream industry ...... 85 E. TSOUKATOS: The private insurance industry in Greece ...... 105 C. TSOUNTAS - V. PANAGOU - TH. PAPAILIAS: Aspects of international monetary co-operation the case of Euro-Markets ...... 123 K. K. CHRISTODOULIDES: Fraud and auditors ...... 137 N. TSOUNπS: Dynamic effects of Polish accession on E.U. Manufacturing ...... 151 ∂. KIKILIA: Mount Athos in Greece and the European Community: The priviliged status and the European Union’s Economic support ...... 167 µπµ§π√∫ƒπ™π∂™ - BOOK REVIEWS ...... 179
ATHENS - A£HNAI, 2003 3 M¤ÏË ™˘Ì‚Ô˘Ï¢ÙÈ΋˜ EÈÙÚÔ‹˜ - Associate Editors
ñ Lazaros Houmanidis (Greece) ñ E. Dinenis (England)
ñ Anna Pellanda (Italy) ñ A.R. Leen (Netherlands)
ñ A. Montesano (Italy) ñ F. Condis y Troiano (Belgium)
ñ G. Viaggi (Italy) ñ Thierry Levy (France)
ñ P. Barucci (Italy) ñ B. Yamey (England)
ñ R. Coppi (Italy) ñ Sheila Dow (England)
ñ A. Rugina (USA) ñ B. Pettman (England)
ñ J. Tarascio (USA) ñ E. Fullbrook (England)
ñ Ingrid Rima (USA) ñ I. Cristescu (Romania)
ñ K. Thanawala (USA) ñ R. Petridis (Australia)
ñ E. Ortiz (Mexico) ñ T. Riha (Australia)
ñ O. Popescu (Argentina) ñ P.J. Gandhi (India)
ñ H. Jenkis (Germany) ñ P. Gemtos (Greece)
ñ U. Witt (Germany) ñ P. Kiochos (Greece) Aگ›ÔÓ OÈÎÔÓÔÌÈ΋˜ IÛÙÔÚ›·˜ / Archives of Economic History, XV/2/2003 5
¶∂ƒπ ∆√À ¢π¶§√°ƒ∞ºπ∫√À ™À™∆∏ª∞∆√™ ∂π™ ∆√ µÀ∑∞¡∆π√¡ §∞∑∞ƒ√™ £. Ã√Àª∞¡π¢∏™ ¶·ÓÂÈÛÙ‹ÌÈÔÓ ¶ÂÈÚ·ÈÒ˜
Abstract Lazaros Th. Houmanidis: On the double - entry system during byzantine times The author of the above article explores two main issues concerning the history of ac- counting: a) whether it was known the use of double - entry in Byzantium, b) the origin of double - entry and its application in the byzantine book - keeping. JEL classification: N00, M41. Keywords: Double - entry system, Byzantine book - keeping,, history of accounting.
1. ∏ ‰ÈÏÔÁÚ·ÊÈ΋ ‹ ‰ÈÁÚ·ÊÈ΋ §ÔÁÈÛÙÈ΋ Ù˘ ÂÔ¯‹˜ ÙˆÓ ‚˘˙·ÓÙÈÓÒÓ ¯ÚfiÓˆÓ Â›Ó·È ı¤Ì· ÙÔ ÔÔ›ÔÓ ··ÈÙ› ÂÚ·ÈÙ¤Úˆ ¤Ú¢ӷÓ. ŒÏÏËÓ˜ Î·È Í¤ÓÔÈ ‚˘˙·ÓÙÈÓÔÏfiÁÔÈ, Î·È Ì¿ÏÈÛÙ· ‰È·ÎÂÎÚÈ̤ÓÔÈ ÌÂٷ͇ ·˘ÙÒÓ, ‰ÂÓ ·Ó·Ê¤ÚÔ˘Ó ÂÚ› ·˘Ù‹˜ ‹ Î·È ÂÏ¿¯ÈÛÙ· ÂȘ Ù· ÁÚ·ÊfiÌÂÓ¿ ÙˆÓ. ŒÙÈ Î·È ÂȘ Ù·˜ ÈÛÙÔÚ›·˜ Ù˘ §ÔÁÈÛÙÈ΋˜ ηıÈÂÚˆÌ¤ÓˆÓ ÂÈÛÙËÌfiÓˆÓ ÂÚ¢ÓËÙÒÓ, ˆ˜ ÔÈ: Melis, Vlamminek, Alfieri, Littleton, Yamey, ∆ofani, de Roover ‰ÂÓ Á›ÓÂÙ·È È‰È·›ÙÂÚË ÌÓ›· ÂÚ› Ù˘ ‰ÈÁÚ·ÊÈ΋˜ §ÔÁÈÛÙÈ΋˜, ÂȘ ÙÔ µ˘˙¿ÓÙÈÔÓ. ∂ÛΤÊıËÓ ÔÏÏ¿ÎȘ Ó· ÌÂÙ·‚Ò ÂȘ ∫ˆÓÛÙ·ÓÙÈÓÔ‡ÔÏÈÓ ÚÔ˜ ‚·ı˘Ù¤Ú·Ó ¤ÚÂ˘Ó·Ó Â› ÙÔ˘ ı¤Ì·ÙÔ˜ ·ÏÏ¿ ¿ÓÙÔÙ ·ÓÂʇÂÙÔ Î¿ÔÈÔ ÛÔ‚·ÚfiÓ ÂÌfi‰ÈÔÓ, ÙÔ ÔÔ›ÔÓ ‰Â ÌÔ˘ ¤ÙÚ ӷ ÂÈÛÎÂÊıÒ ÙËÓ «¶fiÏÈÓ ÙËÓ ∞Á›·Ó». ∂Ș ÙÔ ·ÚfiÓ ¿ÚıÚÔÓ ÌÔ˘ ı· ÚÔÛ·ı‹Ûˆ Ó· ·ÚÔ˘ÛÈ¿Ûˆ, ˆ˜ ÂÎ ÙÔ˘ Ù›ÙÏÔ˘ ÙÔ˘ ı¤Ì·Ùfi˜ ÌÔ˘ ÂÌÊ·›ÓÂÙ·È, ÙËÓ Î·Ù·ÁˆÁ‹Ó Î·È ÙËÓ ÂÊ·ÚÌÔÁ‹Ó ÙÔ˘ ‰ÈÏÔÁÚ·ÊÈÎÔ‡ Û˘ÛÙ‹Ì·ÙÔ˜ ÂȘ ÙÔ µ˘˙¿ÓÙÈÔÓ. ªÂ ÙËÓ §ÔÁÈÛÙÈÎ‹Ó Î·Ù¿ ÙÔÓ ªÂÛ·›ˆÓ·, ËÛ¯ÔÏ‹ıËÛ·Ó, ȉȷÈÙ¤Úˆ˜ ÔÈ: Dino Companino, Giovanni Villani Î·È Alberto Tofani ‰È· Ó· ·ÎÔÏÔ˘ı‹ÛÔ˘Ó ÔÈ: G. Zappa, A. Sapori, F. Melis Ô Î·È ÛÔ˘‰·ÈfiÙÂÚÔ˜ ÙˆÓ 6 §¿˙·ÚÔ˜ £. ÃÔ˘Ì·Ó›‰Ë˜
ÂÚ¢ÓËÙÒÓ Ù˘ §ÔÁÈÛÙÈ΋˜ ηٿ ÙÔÓ ªÂÛ·›ˆÓ·. ∂Î ÙˆÓ ‰È·ÊfiÚˆÓ ÏÔÁÈÛÙÈÎÒÓ ‚È‚Ï›ˆÓ ÙˆÓ ÂÙ·ÈÚÂÈÒÓ ÙˆÓ Bonsignori (Ùˆ¯Â˘Û¿ÓÙˆÓ ÙÔ ¤ÙÔ˜ 1298), ∞lberti (1304-1332) Î·È Peruzzi (Ùˆ¯Â˘Û¿ÓÙˆÓ ÙÔ ¤ÙÔ˜ 1343) Ï·Ì‚¿ÓÔÌÂÓ ÂӉȷÊÂÚÔ‡Û·˜ ÏËÚÔÊÔÚ›·˜ ÂÚ› Ù˘ §ÔÁÈÛÙÈ΋˜, ηٿ ÙÔÓ ªÂÛ·›ˆÓ·, ηıÒ˜ ›Û˘ Î·È ÂÎ ÙˆÓ ‚È‚Ï›ˆÓ Ù˘ ÂÙ·ÈÚ›·˜ ÙÔ˘ Francesco Datini Ì ¤‰Ú·Ó ÙÔ Prato. ∏ §ÔÁÈÛÙÈ΋ ˆÚÈÛÌ¤ÓˆÓ ÂÌÔÚÈÎÒÓ Î·È ∆Ú·Â˙ÈÎÒÓ O›ÎˆÓ, ‰È· ÙËÓ ÂÔ¯‹Ó ÙˆÓ ‹Ùo ·ÚÎÔ‡ÓÙˆ˜ ·ÓÂÙ˘Á̤ÓË1. ¢ÂÓ ‰˘Ó¿ÌÂı· fï˜ Ó· ÈÛ¯˘ÚÈÛıÒÌÂÓ ÙÔ ›‰ÈÔÓ Î·È ‰È· Ù·˜ ‹‰Ë ·Ó·ÊÂÚı›۷˜ ÂÙ·ÈÚ›·˜, ÏËÓ Ù˘ ÙÔ˘ Datini, ˆ˜ ›Û˘ Î·È ‰È· Ù· ÏÔÁÈÛÙÈο ‚È‚Ï›· ÙÔ˘ µÂÓÂÙÔ‡ Andrea Barbarigo (1418 - 1449)2. E›Û˘, Ôχ ÔÏÈÁÒÙÂÚÔÓ ‹ÙÔ ÚÔίˆÚË̤ÓË Ë Ù‹ÚËÛȘ ÏÔÁÈÛÙÈÎÒÓ ‚È‚Ï›ˆÓ ÙˆÓ ÂÌfiÚˆÓ Ù˘ ÿÓÛ·, ÔÈ ÔÔ›ÔÈ Ì¿ÏÈÛÙ· ËÁÓfiÔ˘Ó ÙËÓ ÂÊ·ÚÌÔÁ‹Ó Ù˘ ‰ÈÏÔÁÚ·Ê›·˜ ̤¯ÚÈ ÙÔÓ 16Ô˘ ·ÈÒÓ·3. ∆Ô ›‰ÈÔÓ Â›Û˘ Û˘Ó¤‚·ÈÓÂÓ Î·È Ì ÙÔ˘˜ ÂÌfiÚÔ˘˜ Ù˘ ∆Ô˘ÏÔ‡˙˘ Î·È ÁÂÓÈÎÒ˜ Ì ÙÔ˘˜ °¿ÏÏÔ˘˜ ÂÌfiÚÔ˘˜4. ∂Ó ¿ÛË ÂÚÈÙÒÛÂÈ ÙËÓ §ÔÁÈÛÙÈÎ‹Ó ÂÛ˘ÛÙËÌ·ÙÔÔ›ËÛÂÓ, ηٿ ÙÔÓ 15ÔÓ ·ÈÒÓ·, Ô πÙ·Ïfi˜ Luca Pacciolo (1494) Ì ÙÔ ÂÁ¯ÂÈÚ›‰ÈfiÓ ÙÔ˘ “Summa Aritmentica, Geometria, Proporzione Proporzionalità”, ηıÒ˜ Î·È ¤ÙÂÚÔÈ Û˘ÁÁÚ·Ê›˜, ˆ˜ Ô Lorenzo Chiarini Ì ÙÔ ÂÁ¯ÂÈÚ›‰ÈfiÓ ÙÔ˘ ÂÚ› §ÔÁÈÛÙÈ΋˜ ÂÓÒ ‹‰Ë ÚÔ ·˘ÙÒÓ Â›¯Â ‰ËÌÔÛȇÛË Ô Giovanni di Antonio da Uzzano ÙÔ È‰ÈÎfiÓ ÙÔ˘ ˘fi Ù›ÙÏÔÓ “Pratica della Mercatura” (1442)5. 2. ŸÛÔÓ ·ÊÔÚ¿ ÂȘ ÙÔ Â¿ÁÁÂÏÌ· ÙÔ˘ ÏÔÁÈÛÙÔ‡, ÔÈ ·Ú¯·›ÔÈ ƒˆÌ·›ÔÈ ÙÔÓ ÂοÏÔ˘Ó Ì ÙËÓ Ï¤ÍÈÓ “rationator” Î·È ‚Ú·‰‡ÙÂÚÔÓ “rationarius”. °ÂÓÈÎÒ˜ ÔÈ ·ÛÎÔ‡ÓÙ˜ ÙËÓ §ÔÁÈÛÙÈÎ‹Ó ÂηÏÔ‡ÓÙÔ “rationeri” Î·È Î·Ù¿ ÙÔÓ ªÂÛ·›ˆÓ· “razioneri” Î·È “abacchieri”6. ∞fi ÙÔ˘ 13Ô˘ ·ÈÒÓÔ˜, ‰È·ÚÚ¤ÔÓÙÔ˜ ÙÔ˘ ¯ÚfiÓÔ˘ ÚÔ˜ ÙËÓ ∞Ó·Á¤ÓÓËÛÈÓ, Î·È Î·ÙfiÈÓ, Û˘Ó·ÓÙÒÌÂÓ ÂȘ ÙÔ˘˜ ÌÂÁ¿ÏÔ˘˜ ÂÌÔÚÈÎÔ‡˜ √›ÎÔ˘˜ ÏÔÁÈÛÙ¿˜, fiˆ˜ ‹Û·Ó ÔÈ ÙˆÓ :Francesco Datini, Alfredo di Giudice, Pe- ruzzi, Bardi Î.¿. ™Ô˘‰·›Ô˘˜ ÏÔÁÈÛÙ¿˜ ÌÂٷ͇ ÙÔ‡ÙˆÓ ı· ·Ó·Ê¤Úˆ ÙÔÓ Francesco Boducci (1301), ÙÔÓ Francesco di Balduccio Pegolotti, ÙÔÓ Francesco Doldacio (1342) Î·È ÙÔ˘˜ ‹‰Ë ÌÓËÌÔÓ¢ı¤ÓÙ·˜ Lorenzo Chiari- ni (1418) Î·È Giovanni di Antonio da Uzzano7. ∂›Û˘, ηٿ ÙËÓ ·˘Ù‹Ó ÂÚ›Ô‰ÔÓ ˘‹Ú¯ÔÓ Î·È ÏÔÁÈÛÙ·›, ÔÈ ÔÔ›ÔÈ ÂÙ‹ÚÔ˘Ó Ù· ÏÔÁÈÛÙÈο ‚È‚Ï›· ÙÔ˘ ¢ËÌÔÛ›Ô˘, ˆ˜ ÙÔ‡ÙÔ Û˘Ó¤‚·ÈÓÂÓ Î·È ÂȘ ÙÔ µ˘˙¿ÓÙÈÔÓ, ÂȘ ÙÔ ÔÔ›ÔÓ ÂÈÊÔÚÙÈṲ̂ÓÔ˜ ÚÔ˜ ÙÔÓ ÛÎÔfiÓ ·˘ÙfiÓ ‹ÙÔ Ô §ÔÁÔı¤Ù˘ ÙÔ˘ °ÂÓÈÎÔ‡ ÙËÚÒÓ Ù· ÏÔÁÈÛÙÈο ‚È‚Ï›· › ÙˆÓ ÂÛfi‰ˆÓ Î·È ÙˆÓ ÂÍfi‰ˆÓ ÙÔ˘ ¶ÂÚ› ÙÔ˘ ‰ÈÏÔÁÚ·ÊÈÎÔ‡ Û˘ÛÙ‹Ì·ÙÔ˜ ÂȘ ÙÔ µ˘˙¿ÓÙÈÔÓ 7
∫Ú¿ÙÔ˘˜8. ∫·Ù’ ·Ú¯‹Ó ÙËÓ ÏÔÁÈÛÙÈÎ‹Ó ÂÙ‹ÚÔ˘Ó ÔÈ ›‰ÈÔÈ ÔÈ ÂȯÂÈÚËÌ·Ù›·È, Î·È Â›Ù· Ì ÙËÓ ¿ÚÔ‰ÔÓ ÙÔ˘ ¯ÚfiÓÔ˘ ÔÈ ÏÔÁÈÛÙ·›. ∏ §ÔÁÈÛÙÈ΋ ÂÍÂÈÏ›¯ıË. ∆· ‰Â §ÔÁÈÛÙÈο ‚È‚Ï›· ¤ÁÈÓ·Ó ÂÚÈÛÛfiÙÂÚ· ¤ÓÂη ˆÓ ÂȉÈÎÒÓ ÏÔÁ·ÚÈ·ÛÌÒÓ. ∏ ÙÔÈ·‡ÙË ÂͤÏÈÍȘ Ù˘ §ÔÁÈÛÙÈ΋˜ η٤ÏËÍÂÓ ÂȘ ÙËÓ ·Ó·Î¿Ï˘„ÈÓ ÙÔ˘ ‰ÈÏÔÁÚ·ÊÈÎÔ‡ ‹ ‰ÈÁÚ·ÊÈÎÔ‡ Û˘ÛÙ‹Ì·ÙÔ˜ Î·È Ë ÔÔ›· ÚÔÛ¤‰ˆÛÂÓ ·Ó¿Ù˘ÍÈÓ, ηٿ Werner Sombart, ÂȘ ÙËÓ Î·ÈÙ·ÏÈÛÙÈÎ‹Ó Âȯ›ÚËÛÈÓ9. 3. ªÂٷ͇ 13Ô˘ - 15Ô˘ ·ÈÒÓÔ˜ Ë πÙ·ÏÈ΋ ÃÂÚÛfiÓËÛÔ˜ ‰È¤Ú¯ÂÙ·È ÂÚ›Ô‰ÔÓ ÂÓÙfiÓÔ˘ ÔÈÎÔÓÔÌÈ΋˜ ‰Ú·ÛÙËÚÈfiÙËÙÔ˜, Ë ÔÔ›· Î·È ÂÂÎÙ›ÓÂÙ·È, ¤ÙÈ ÂÚÈÛÛfiÙÂÚÔÓ, Ì ÙËÓ ªÂÛÔÁÂÈ·Î‹Ó ÂÓfiÙËÙ·, ÌÂÙ¿ ÙËÓ ˘Ô¯ÒÚËÛÈÓ ÙÔ˘ ∞Ú·‚ÈÎÔ‡ ÎfiÛÌÔ˘. ∫·Ù¿ ÙËÓ ÂÔ¯‹Ó ·˘Ù‹Ó, ·Ó·‰ÂÈÎÓ‡ÔÓÙ·È ÂȘ ÛÔ˘‰·›· ÂÌÔÚÈο ΤÓÙÚ· Ë Lucca Î·È ÙÔ Bari, ÔÓÔÌ·ÛÙ·› fiÏÂȘ ‰È· ÙËÓ ÌÂÙ·ÍÔ·Ú·ÁˆÁ‹Ó ÙˆÓ. ∆Ô ªilano ›Û˘, ·fi 13Ô˘ ·ÈÒÓÔ˜, η٤ÛÙË ‚·ÛÈÎfiÓ Î¤ÓÙÚÔÓ ÙÔ˘ ÂÌÔÚ›Ô˘ Ù˘ §ÔÌ‚·Ú‰›·˜ Ì ÙÔ˘˜ ÂÓ ·˘ÙÒ ÌÂÁ¿ÏÔ˘˜ ÂȯÂÈÚËÌ·Ù›·˜ Alberti di Giudice Î·È ÛÔ˘‰·›Ô˘˜ ÍÂÓÔ‰fi¯Ô˘˜ Î·È ÓÔÌÈÎÔ‡˜, ÔÈ ÔÔ›ÔÈ ·¤ÎÙËÛ·Ó ÌÂÁ¿Ï·˜ ÂÚÈÔ˘Û›·˜10. ¶ÏËÓ fï˜ ÙÔ‡ÙˆÓ, Û˘Ó Ùˆ ¯ÚfiÓˆ ÂÓÂÊ·Ó›ÛıËÛ·Ó Î·È ÔÓÔÌ·ÛÙÔ› ∆Ú·Â˙›Ù·È ˆ˜ ÔÈ: G. Galeazzo, P. Maniza, A. De Monte, P. Da Osnago, G. Taverna11. ∂›Û˘, ·Ó·‰ÂÈÎÓ‡ÔÓÙ·È ÂȘ ÌÂÁ¿ÏÔ˘˜ ÂȯÂÈÚËÌ·Ù›·˜ ÔÈ ÌÂÁ·Ï¤ÌÔÚÔÈ Ù˘ Ó·˘ÙÈ΋˜ fiψ˜ Amalfi Î·È ÌÂٷ͇ ÙÔ‡ÙˆÓ Ô Mauro Î·È Ô Pantaleone, ÔÈ ÔÔ›ÔÈ ‹Ù·Ó ÔÓÔÌ·ÛÙÔ› ÂȘ ÙËÓ ∫ˆÓÛÙ·ÓÙÈÓÔ‡ÔÏÈÓ Ì ٷ ÂΛ Ú·ÎÙÔÚ›· ÙˆÓ Î·È ÂȯÂÈÚ‹ÛÂȘ ÙˆÓ. O˘¯ ‹ÙÙÔÓ ÔÓÔÌ·ÛÙÔ› ‹Û·Ó Î·È ÔÈ ¤ÌÔÚÔÈ Ù˘ ºÏˆÚÂÓÙ›·˜ Bardi Î·È Frescobaldi. ŸÏÔÈ ÔÈ ·ÓˆÙ¤Úˆ ·Ó·ÊÂÚı¤ÓÙ˜ ¯ÚËÛÈÌÔÔ›Ô˘Ó ÏÔÁÈÛÙ¿˜ Î·È ÏÔÁÈÛÙÈÎfiÓ Û¯¤‰ÈÔÓ Ì ÏÔÁÈÛÙÈο ‚È‚Ï›·, ÂÚ› ÙˆÓ ÔÔ›ˆÓ ı· ÔÌÈÏ‹ÛˆÌÂÓ ÂÓ Û˘Ó¯›·. ∂›Û˘, ÏËÓ ÙˆÓ ·Ó·ÊÂÚı¤ÓÙˆÓ ÂÌÔÚÈÎÒÓ Î¤ÓÙÚˆÓ ÔÓÔÌ·ÛÙ¿ ‹Û·Ó Î·È ·È fiÏÂȘ: ¶›˙·, µÂÓÂÙ›·, °ÂÓÔ‡Ë, ∆Ú¿ÓÈ Î.¿. ∂Î ÙˆÓ ‰È·ÊfiÚˆÓ ÂȉÒÓ ÂÌÔÚ›Ô˘ ·È Û˘Ó·ÏÏ·Á·›, ÂÓ µ˘˙·ÓÙ›ˆ, ÂÁ›ÓÔÓÙÔ ÂȘ ÛÎÂ‡Ë Î·È ÏÂÈ„·ÓÔı‹Î·˜, ÔχÙÈÌ· ÂÓ‰‡Ì·Ù· Î·È fi,ÙÈ ¿ÏÏÔ ÂÌfiÚÂ˘Ì· ¿ÓËÎÂÓ ÂȘ Ù· ÌË ÎˆÏ˘fiÌÂÓ·12. √È Ô›ÓÔÈ Ù˘ ∫‡ÚÔ˘, Ù˘ ƒfi‰Ô˘, Ù˘ °·ÏÏ›·˜, Ù˘ °ÂÚÌ·Ó›·˜ Ù· ÁÔ˘Ó·ÚÈο Î·È ·ÛÙ¿ Ù˘ ª·‡Ú˘ £·Ï¿ÛÛ˘ Î.¿. ‹Û·Ó ·ÓÙÈΛÌÂÓ· ÙÔ˘ ÂÎÙÂٷ̤ÓÔ˘ ‚˘˙·ÓÙÈÓÔ‡ ÂÌÔÚ›Ô˘, ΢ڛˆ˜ ‰Â ÙÔ ÂÌfiÚÈÔÓ ÙˆÓ ÌÂٷ͈ÙÒÓ, ÙÔ ÔÔ›ÔÓ Î·Ù¿ Fanfani Û˘ÓÂÙ¤ÏÂÛ ‰È· Ó· ·Ê˘ÓÈÛı‹ Ë ÔÈÎÔÓÔÌ›·,13 ÌÂÙ¿ ÙËÓ ÂÚ›Ô‰ÔÓ ÓÂÎÚÒÛÂÒ˜ Ù˘ (9Ô˜ - 11Ô˜ ·ÈÒÓ). ∆Ô ÂÌfiÚÈÔÓ ÌÂٷ͇ ∞Ó·ÙÔÏ‹˜ Î·È ¢‡Ûˆ˜, ‰ÈÂÍ‹ÁÂÙÔ Ì¤Ûˆ 8 §¿˙·ÚÔ˜ £. ÃÔ˘Ì·Ó›‰Ë˜
∫ˆÓÛÙ·ÓÙÈÓÔ˘fiψ˜, ÔÈ ‰Â πÙ·ÏÔ› ¤ÌÔÚÔÈ ÂÊ·ÚÌfi˙ÔÓÙ˜ ÙËÓ ‰ÈÏÔÁÚ·ÊÈÎ‹Ó Ì¤ıÔ‰ÔÓ ÙËÓ Î·Ù¤ÛÙËÛ·Ó ÁÓˆÛÙ‹Ó Î·È ÂȘ ÙÔ˘˜ ŒÏÏËÓ·˜. 4. ∫·Ù¿ ÙÔÓ 13ÔÓ ·ÈÒÓ· Ô ¯¿ÚÙ˘ ÂÈÎÚ·Ù› › ÙÔ˘ ·‡ÚÔ˘, Ô ÔÔ›Ô˜ ÂÍ·ÎÔÏÔ˘ı› Ó· ¯ÚËÛÈÌÔÔÈ‹Ù·È ÌfiÓÔÓ ‰È· ÙÔ È‰È·›ÙÂÚÔÓ ‚È‚Ï›ÔÓ ÙÔ˘ ÂȯÂÈÚËÌ·Ù›Ô˘. ∆· ÏÔÁÈÛÙÈο ‚È‚Ï›· ‹Û·Ó ÎÂÎ·Ï˘Ì̤ӷ Ì ÂÚÁ·ÌËÓ‹Ó Î·È ‰¤ÚÌ· ËÚ›ıÌÔ˘Ó ‰Â ̤¯ÚÈ Î·È 1.000 ÛÂÏ›‰·˜. √ ¯ÚËÛÈÌÔÔÈÔ‡ÌÂÓÔ˜ ‰È’ ·˘Ù¿ ¯¿ÚÙ˘ ‹ÙÔ ‰È·ÛÙ¿ÛÂˆÓ 29 45 (libri mezzani) , ηıÒ˜ ›Û˘ Î·È ¯¿ÚÙ˘ ‰ÈÏ·Û›·˜ ‰È·ÛÙ¿Ûˆ˜ (libri reali)14. ∆Ô ∫·ıÔÏÈÎfiÓ Î·È ÙÔ ‚È‚Ï›ÔÓ ÙˆÓ ∂ÌÔÚÂ˘Ì¿ÙˆÓ ˘Â›ÁÔÓÙÔ ÂȘ ÙËÓ ·˘Ù‹Ó ηÙËÁÔÚ›·Ó ÌÂÁ¤ıÔ˘˜ ¯¿ÚÙÔ˘, ÂÓÒ ‰È· ÙËÓ ·ÏÏËÏÔÁÚ·Ê›·Ó Î·È ÙÔ ËÌÂÚÔÏfiÁÈÔÓ (giornale) Ô ¯¿ÚÙ˘ ‹ÙÔ ÌÈÎÚÔÙ¤ÚÔ˘ ÌÂÁ¤ıÔ˘˜. ∆· ‚È‚Ï›· ¿ÓÙˆ˜ ‰ÂÓ ˘¤ÎÂÈÓÙÔ ÂȘ ÛÙ·ıÂÚ¿˜ ‰È·ÛÙ¿ÛÂȘ15. ¶ÚÔÛ¤ÙÈ Â¯ÚËÛÈÌÔÔÈÔ‡ÓÙÔ Î·È ¤ÙÂÚ· ‚È‚Ï›· ÂȉÈÎÒÓ ÏÔÁ·ÚÈ·ÛÌÒÓ Î·È ÙÂÙÚ¿‰È·. √ ÂȯÂÈÚËÌ·Ù›·˜ ‰È¤ıÂÙÂÓ Â›Û˘ -ˆ˜ ‹‰Ë ·ÓÂʤÚıË- ȉÈÎfiÓ ÙÔ˘ ‚È‚Ï›ÔÓ (libro segreto), ÙÔ ÔÔ›ÔÓ ÂʇϷÛÛÂÓ ÂȘ ÙËÓ ÔÈΛ·Ó ÙÔ˘, ÁÂÓÈÎÒ˜ ‰Â Ù· ‚È‚Ï›· ÂÙ›ıÂÓÙÔ ÂȘ ÂȉÈο ÂÚÌ¿ÚÈ· ηٷÛ΢·Ṳ̂ӷ ‰›ÎËÓ ÂÚÈÛÙÂÚÂÒÓÔ˜ ÂȘ Ù· ÁÚ·Ê›· Ù˘ ÂÙ·ÈÚ›·˜16. Õ·ÓÙ· Ù· ‚È‚Ï›· ‹Û·Ó ËÚÈıÌË̤ӷ Î·È ¤ÊÂÚÔÓ Â’ ·˘ÙÒÓ ‰È·ÎÚÈÙÈÎfiÓ Û‡Ì‚ÔÏÔÓ. ¢È· ÙÔ ÛÙ¤Áӈ̷ ‰Â Ù˘ ÌÂÏ¿Ó˘, ÙˆÓ Ê‡ÏÏˆÓ ÙˆÓ Â¯ÚËÛÈÌÔÔÈ›ÙÔ ÎfiÓȘ, ÂÓÒ Ë ÁÚ·Ê‹ ÂÁ›ÓÂÙÔ Ì ¤ÓÓ·˜ ÂÎ ÙÂÚÔ‡, ÙˆÓ ÔÔ›ˆÓ ÔÓÔÌ·ÛÙ·› ‹Û·Ó ·È Ù˘ ∆ÔÛοÓ˘. √È ÏÔÁ·ÚÈ·ÛÌÔ› ‹Û·Ó ηٷ¯ˆÚË̤ÓÔÈ ÂȘ ‰‡Ô ÙÌ‹Ì·Ù·: ¯ÚÂÒÛˆ˜ ‰ËÏ. ÂÈÛ·ÁˆÁ‹˜ (entrata) Î·È ÈÛÙÒÛˆ˜ ‰ËÏ. ÂÍ·ÁˆÁ‹˜ (uscita) Î·È Ë ‰È·›ÚÂÛȘ ·‡ÙË Û˘Ó·ÓÙ¿Ù·È ÙÔ ÚÒÙÔÓ ÂȘ ™È¤Ó· (1277-1288) Î·È ÂȘ ºÏˆÚÂÓÙÈÓfiÓ ∆Ú·Â˙›ÙËÓ ÂÚÁ·˙fiÌÂÓÔÓ ÂȘ ÙËÓ µologna17. √È ÏÔÁ·ÚÈ·ÛÌÔ› ÙÔ˘ ∫·ıÔÏÈÎÔ‡ (libro grande, mastro) ÌÂÙÂʤÚÔÓÙÔ ÂȘ ȉȷÈÙ¤ÚÔ˘˜ ÂȉÈÎÔ‡˜ ÏÔÁ·ÚÈ·ÛÌÔ‡˜, Î·È ·ÔÙ¤ÏÂÛÌ· Ù˘ ÙÔÈ·‡Ù˘ ¯Ú‹ÛÂÒ˜ ÙÔ˘ ˘‹ÚÍÂÓ Î·È Ë ·ÈÙ›· Ù˘ ÙËÚ‹Ûˆ˜ Ù˘ ‰ÈÏÔÁÚ·ÊÈ΋˜ ÌÂıfi‰Ô˘ Î·È ÙÔ˘ ÈÛÔ˙˘Á›Ô˘ ÏÔÁ·ÚÈ·ÛÌÒÓ. ∏ ‰ÈÏÔÁÚ·Ê›·, Û˘ÌÊÒÓˆ˜ ÚÔ˜ ÙÔÓ Melis, ÂÊËÚÌfiÛıË ÂÚ› ÙÔ Ù¤ÏÔ˜ ÙÔ˘ 13Ô˘ ·ÈÒÓÔ˜ ˘fi Ù˘ ÂÙ·ÈÚ›·˜ ÙÔ˘ Ugolini ÂȘ ™È¤ÓËÓ18. ∂Ó Û˘Ó¯›· ÙËÓ Û˘Ó·ÓÙÒÌÂÓ ÂȘ ÙËÓ ÂÓ ∫·Ì·Ó›· ÂÙ·ÈÚ›·Ó ÙÔ˘ Ranieri Fini (1291 - 1305), ÂȘ ÙËÓ ÂÙ·ÈÚ›·Ó Giovanni Farolfi (1299 - 1300), ›Û˘ ÂȘ ÙËÓ ÂÙ·ÈÚ›·Ó Alberti di Giudice (1302 - 1332), ÂȘ ÙËÓ ÂÙ·ÈÚ›·Ó Frescoboldi (1305 - 1390), Î·È ÂȘ ÙËÓ ÂÙ·ÈÚ›·Ó Barli (1310 - 1398). ¶ÏËÓ fï˜ ÙˆÓ ÂÓ ÏfiÁˆ ÂÙ·ÈÚÂÈÒÓ Î·È Ë ÙÔ˘ Jachomo Badoer ‰ÈÂÙ‹ÚÂÈ ÏÔÁÈÛÙÈÎ‹Ó Â› ÙË ¶ÂÚ› ÙÔ˘ ‰ÈÏÔÁÚ·ÊÈÎÔ‡ Û˘ÛÙ‹Ì·ÙÔ˜ ÂȘ ÙÔ µ˘˙¿ÓÙÈÔÓ 9
‚¿ÛÂÈ ÙÔ˘ ‰ÈÏÔÁÚ·ÊÈÎÔ‡ Û˘ÛÙ‹Ì·ÙÔ˜, ÙÔ ÔÔ›ÔÓ ÚԤ΢„ ÂÎ Ù˘ Û˘Ó‰˘·ÛÙÈ΋˜ ÂÁÁÚ·Ê‹˜ ÙÔ˘ ∫·ıÔÏÈÎÔ‡, ¯·Ú·ÎÙËÚÈÛÙÈÎfiÓ ÙËÚ‹Ûˆ˜ ÙÔ˘ ÂÓ ∆ÔÛοÓË, ηٿ ÙÔ ‰Â‡ÙÂÚÔÓ ËÌ›ÛË ÙÔ˘ 14Ô˘ ·ÈÒÓÔ˜ (Melis, 1962, ÛÂÏ. 424, Peragallo, 1983, ÛÂÏ. 99), ˆ˜ ›Û˘ Î·È Ô Francesco Datini (1318 - 1324) ÂȘ Ù· ·Ú¯Â›· Ù˘ ÂÙ·ÈÚ›·˜ ÙÔ˘ ÔÔ›Ô˘ Ô Melis, ·ÓÂÎ¿Ï˘„ Ï›ÛÙ· fiÛ· ÛÙÔȯ›· ‰È· Ó· Ú›„Ë Êˆ˜ ÁÂÓÈÎÒÙÂÚÔÓ ÂȘ ÙËÓ √ÈÎÔÓÔÌ›·Ó ÙÔ˘ ªÂÛ·›ˆÓÔ˜. ∂Ș ÙËÓ §ÔÁÈÛÙÈÎ‹Ó ÙˆÓ ÂÙ·ÈÚÂÈÒÓ, Ù·˜ ÔÔ›·˜ ·ÓÂʤڷÌÂÓ ÂÚÈÏ·Ì‚¿ÓÔÓÙ·È Î·È ÏÔÁ·ÚÈ·ÛÌÔ› ·ÊÔÚÒÓÙ˜ ÂȘ ÙÔ Ú¢ÛÙfiÓ ¯Ú‹Ì·19, ÙÔ Û˘Ó¿ÏÏ·ÁÌ·20, ÙËÓ ÂÈÙ·Á‹Ó21, ÙËÓ ÔÈÛıÔÁÚ·ÊË̤ÓËÓ Û˘Ó·ÏÏ·ÁÌ·ÙÈ΋Ó22, ÙÔ ÙÚ·Â˙ÈÎfiÓ ÁÚ·ÌÌ¿ÙÈÔÓ23, ÙËÓ Ù‹ÚËÛÈÓ ÏÔÁ·ÚÈ·ÛÌÔ‡ Á‡ÚÔ˘ Î·È ·ÓÔ›ÁÌ·ÙÔ˜ ÈÛÙÒÛÂˆÓ ÙÚÂ¯Ô˘Ì¤ÓˆÓ ÏÔÁ·ÚÈ·ÛÌÒÓ ÚÔ˜ fiÊÂÏÔ˜ ÙÚ›ÙˆÓ24. °ÂÁÔÓfi˜ ¿ÓÙˆ˜ Â›Ó·È fiÙÈ Ù· ÏÔÁÈÛÙÈο ‚È‚Ï›· ‰ÂÓ ÂÌÊ·Ó›˙Ô˘Ó ˆÚÈÌfiÙËÙ· ÙËÚ‹ÛÂÒ˜ ÙˆÓ ÚÔ ÙÔ˘ ¤ÙÔ˘˜ 1400. ∫·È Ë ‰È·ÊÔÚ¿ ·˘Ù‹ ηı›ÛÙ·Ù·È ÂÌÊ·Ó‹˜, fiÙ·Ó Û˘ÁÎÚ›ÓˆÌÂÓ Ù· ÏÔÁÈÛÙÈο ‚È‚Ï›· ÙÔ˘ √›ÎÔ˘ Peruzzi Ì ٷ ÌÂÙ·ÁÂÓ¤ÛÙÂÚ· ÙÔ˘ Datini25. √‡ÙÔ˜ ÌÂÙ¿ ÙÔ˘ Badoer Î·È ¿ÏÏˆÓ πÙ·ÏÒÓ ÌÂÁ·ÏÂÌfiÚˆÓ Û˘Ó¿ÁÂÙ·È fiÙÈ Î·Ù¤ÛÙËÛ·Ó ÁÓˆÛÙ‹Ó ‰È· ÙˆÓ ÂÓ ∫ˆÓÛÙ·ÓÙÈÓÔ˘fiÏÂÈ Ú·ÎÙÔÚ›ˆÓ ÙˆÓ ÂÙ·ÈÚÂÈÒÓ ÙˆÓ ÙËÓ ‰ÈÏÔÁÚ·Ê›·Ó ÂȘ ÙÔ µ˘˙¿ÓÙÈÔÓ. 5. ∂Ș ÙÔ µ˘˙¿ÓÙÈÔÓ Ë ‰ÈÏÔÁÚ·ÊÈ΋ ̤ıÔ‰Ô˜ Û˘ÓÂÒ˜ fi¯È ÌfiÓÔÓ ÂÊËÚÌfi˙ÂÙÔ ˘fi ÙˆÓ È‰ÈˆÙÒÓ ÂÌfiÚˆÓ ·ÏÏ¿, ˆ˜ ‹‰Ë ÂϤ¯ıË, Î·È ˘fi. ÙÔ˘ §ÔÁÔı¤ÙÔ˘ ÙÔ˘ °ÂÓÈÎÔ‡ ¶ÚÔ˚Ûٷ̤ÓÔ˘ ÙÔ˘ §ÔÁÈÛÙËÚ›Ô˘ ÙÔ˘ ∫Ú¿ÙÔ˘˜26. ™˘Ó‹ıˆ˜ ‰Â Ë ÔÚÔÏÔÁ›· ηٿ Ù·˜ ÏÔÁÈÛÙÈο˜ Ú¿ÍÂȘ ÂÁÚ¿ÊÂÙÔ ÂȘ ÈÙ·ÏÈÎ‹Ó ÁÏÒÛÛ·Ó27. ∏ ‚˘˙·ÓÙÈÓ‹ √ÈÎÔÓÔÌ›· ‹ÙÔ Î·Ù¿ ‚¿ÛÈÓ ÁˆÚÁÈ΋ ·ÏÏ¿ Î·È ·ÚÎÔ‡ÓÙˆ˜ ·ÛÙÈÎÔ-ÂÌÔÚÈ΋ ÒÛÙ ӷ Û˘ÁÎÂÓÙÚÒÓÔÓÙ·È ÎÂÊ¿Ï·È· ÂÎ ÙÔ˘ ˘fi ÙÔ˘ ÂÌÔÚ›Ô˘ ‰È·ÎÈÓÔ˘Ì¤ÓˆÓ ÂÌÔÚÂ˘Ì¿ÙˆÓ ÂÓÙfi˜ Î·È ÂÎÙfi˜ Ù˘ ·˘ÙÔÎÚ·ÙÔÚ›·˜. ∫·Ù¿ Û˘Ó¤ÂÈ·Ó Ë §ÔÁÈÛÙÈ΋ ‹ÙÔ ··Ú·›ÙËÙÔ˜ ÂȘ ÙÔ˘˜ ÂÌfiÚÔ˘˜. ¢˘ÛÙ˘¯Ò˜ ‰ÂÓ ¤¯ÔÌÂÓ Û·Ê›˜ ÏËÚÔÊÔڛ˜ ÂÚ› ·˘Ù‹˜, Ô‡Ù fï˜ Î·È ‰È· ÙÔ˘˜ ·ÁÁÂÏÌ·Ù›·˜ ÏÔÁÈÛÙ¿˜ Î·È ÙËÓ ·ÌÔÈ‚‹ ÙˆÓ ÂȘ ÙÔ µ˘˙¿ÓÙÈÔÓ. ∆· ·Ó·ÊÂÚfiÌÂÓ· ˘fi ÙÔ˘ ∫.π. ∞Ì¿ÓÙÔ˘ (¶ÂÚ› ∂ÌÌ·ÓÔ˘‹Ï °Ï˘Ù˙Ô˘Ó›Ô˘, «∆· °Ú¿ÌÌ·Ù· ÂȘ Ã›Ô˘ ηٿ ÙËÓ ∆Ô˘ÚÎÔÎÚ·Ù›·Ó», ¶ÂÈڷȇ˜ 1946 ÛÂÏ. ÛÂÏ. 64-65), ηıÒ˜ Î·È Ù· ˘fi ÙÔ˘ ›‰ÈÔ˘ «∏ §ÔÁ·ÚÈ·ÛÙÈ΋ ÙÔ˘ °Ï˘Ù˙Ô˘Ó›Ô˘» «∏ÌÂÚÔÏfiÁÈÔÓ Ù˘ ªÂÁ¿Ï˘ ∂ÏÏ¿‰Ô˜», 1934 ÛÂÏ. ÛÂÏ. 179-184 Â›Ó·È ÛËÌ·ÓÙÈο ·ÏÏ¿ ÂÏ¿¯ÈÛÙ· -¤ÙÈ Î·È Ù· ˘fi ÙÔ˘ Paul Colat ·Ó·ÊÂÚfiÌÂÓ· (Nouveaux manuscrits copies par Emmanuel 10 §¿˙·ÚÔ˜ £. ÃÔ˘Ì·Ó›‰Ë˜
Glytzounis, «∂ÏÏËÓÈ΋ ∂Ù·ÈÚ›· µ˘˙·ÓÙÈÓÒÓ ™Ô˘‰ÒÓ» 1972-1973 ÛÂÏ. ÛÂÏ. 39-40- ÙÔ ›‰ÈÔÓ Î·È Ë ·Ó·ÊÔÚ¿ ÙËÓ ÔÔ›·Ó οÌÓÂÈ ‰È· ÙËÓ √ÈÎÔÓÔÌ›·Ó Ù˘ Ã›Ô˘ › ‚˘˙·ÓÙÈÓÒÓ ¯ÚfiÓˆÓ, fiˆ˜ ¤¯ˆÌÂÓ ÏËÚÔÊÔÚ›·˜ Î·È ÂÎ ‰Â˘ÙÂÚÔÁÂÓÒÓ ËÁÒÓ). µÂ‚·›ˆ˜ ¿·Û·È ·È ÚÔÛ¿ıÂÈ·È Ù·˜ ÔÔ›·˜ ·ÓÂʤڷÌÂÓ Â›Ó·È ·ÍÈfiÏÔÁÔÈ, ÙÔ ı¤Ì· fï˜ ··ÈÙ› ‚·ı˘Ù¤Ú·Ó ¤Ú¢ӷÓ. ∫·Ù¿ ÙËÓ ÁÓÒÌËÓ ÌÔ˘, ı· ¤Ú ӷ ‰Ôı‹ ÂȯÔÚ‹ÁËÛȘ ÂȘ ‰È·ÎÂÎÚÈ̤ÓÔ˘˜ ÂÚ¢ÓËÙ¿˜ ÙÔ˘ µ˘˙·ÓÙ›Ô˘ ‰È· Ó· ÌÂÙ·‚Ô‡Ó ÂȘ ∫ˆÓÛÙ·ÓÙÈÓÔ‡ÔÏÈÓ ÚÔ˜ Â͇ÚÂÛÈÓ ÚˆÙÔÁÂÓÒÓ ËÁÒÓ Û¯ÂÙÈÎÒ˜ Ì ÙËÓ §ÔÁÈÛÙÈ΋Ó, Î·È È‰È·ÈÙ¤Úˆ˜ ‰È· ÙËÓ ‰ÈÏÔÁÚ·ÊÈÎ‹Ó ÂȘ ÙÔ µ˘˙¿ÓÙÈÔÓ. ¶Èı·ÓfiÓ Ó· ¤¯ˆÌÂÓ ÛÔ˘‰·›·˜ ÏËÚÔÊÔÚ›·˜ Î·È ÂÎ ÙˆÓ ÏÔÁÈÛÙÈÎÒÓ ‚È‚Ï›ˆÓ ÙÔ˘ ÂÚ›ÊËÌÔ˘ ÔÏ˘Î·Ù·ÛÙ‹Ì·ÙÔ˜ ÙˆÓ ‚˘˙·ÓÙÈÓÒÓ ¯ÚfiÓˆÓ §·ÌÙ‹Ú ‹ §·ÌÙ‹ÚÈÔ˜ √›ÎÔ˜, ˆ˜ ÙÔ‡ÙÔ˜ ÂηÏ›ÙÔ, ¤ÓÂη ÙÔ˘ ÁÂÁÔÓfiÙÔ˜ fiÙÈ Âʈٛ˙ÂÙÔ Î·ı’ fiÏËÓ ÙËÓ ‰È¿ÚÎÂÈ·Ó Ù˘ Ó˘ÎÙfi˜, Ì ÙÔ Ï‹ıÔ˜ Ù˘ ÂÏ·Ù›·˜ ÙÔ˘, Î·È Ù˘ ÔÈÎÈÏ›·˜ ÙˆÓ ÂÌÔÚÂ˘Ì¿ÙˆÓ ÙÔ˘. 6. ªÂÙ¿ ÙËÓ ·ÔÊÚ¿‰·Ó 29ËÓ ª·˝Ô˘ 1453 ÙÒÛÈÓ Ù˘ ‚·ÛÈÏ¢ԇÛ˘, Î·È Ù˘ ÂÓ Û˘Ó¯›· ηٷÎÙ‹Ûˆ˜ ÔÏÔÎÏ‹ÚÔ˘ Ù˘ ∂ÏÏ¿‰Ô˜ ˘fi ÙˆÓ ∆Ô‡ÚΈÓ, Ë √ÈÎÔÓÔÌ›· ·ÚÔ˘Û›·Û ·Ó·ÈÌ›·Ó. ¢ÈfiÙÈ Î·Ù¿ ÙËÓ ‰È¿ÚÎÂÈ·Ó Ù˘ ‰Ô˘Ï›·˜, ÔÈ ŒÏÏËÓ˜, ‰ÂÓ Ë‰˘Ó‹ıËÛ·Ó Ó· ·Ó·Ù˘¯ıÔ‡Ó ÔÈÎÔÓÔÌÈÎÒ˜. ∞fi ÙÔ˘ 18Ô˘ ·ÈÒÓÔ˜ fï˜ Î·È Î·ÙfiÈÓ, ÔÈ ŒÏÏËÓ˜, ¤ÛÙˆ Î·È ˘fi ηٿÎÙËÛÈÓ ÙÂÏÔ‡ÓÙ˜, ·Ó·Ù‡ÛÛÔ˘Ó ÙËÓ ÂÌÔÚÈÎ‹Ó ÙˆÓ Ó·˘ÙÈÏ›·Ó, Î·È ÌÂÙ¤Ú¯ÔÓÙ·È ‰È¿ÊÔÚ· ·ÁÁ¤ÏÌ·Ù·. ∏ √ÚıÔ‰ÔÍ›· Î·È Ë ÂÏÏËÓÈ΋ ÂÌÔÚÈ΋ Ó·˘ÙÈÏ›· ÂÓ›Û¯˘Û·Ó Ù· Û¤ÚÌ·Ù· Ù˘ ·ӷÛÙ¿ÛÂÒ˜ Ì·˜ Î·È ÙËÓ ›ÛÙÈÓ Ì·˜ ‰È· ÙËÓ ·ÂÏ¢ı¤ÚˆÛÈÓ ÙÔ˘ ŒıÓÔ˘˜. ¶·Ú¿ ÙËÓ ·Ê‡ÓÈÛÈÓ Ù˘ √ÈÎÔÓÔÌ›·˜ Ì·˜, fï˜, Ë §ÔÁÈÛÙÈ΋ ‰ÂÓ Â¯ÚËÛÈÌÔÔÈ‹ıË ˘fi ÙˆÓ ∂ÏÏ‹ÓˆÓ ÂÌfiÚˆÓ Î·È ÏÔÈÔÎÙËÙÒÓ, Î·È ·Ú¤ÌÂÈÓÂÓ ÂȘ ÙËÓ ÚˆÙfiÁÔÓÔÓ ¯Ú‹ÛÈÓ ÙÔ˘ ÓÙÂÊÙ¤Ú (‰ÂÊÙ¤ÚÈ)28. ¶ÏËÓ fï˜ ÙÔ˘ ÓÙÂÊÙ¤Ú ÂÙ‹ÚÔ˘Ó Î·È ÙÔ Î·Ù¿ÛÙȯÔÓ, ÙÔ ÔÔ›ÔÓ ˘Ô‰È·ÈÚ›ÙÔ ÂȘ ÌÈÎÚfiÙÂÚ· ηٿÛÙȯ·, ÙˆÓ ÔÔ›ˆÓ ÙÔ ÛÔ˘‰·ÈfiÙÂÚÔÓ Î·È ıˆÚÔ‡ÌÂÓÔÓ Ì‹ÙËÚ ÙˆÓ ÌÈÎÚÔÙ¤ÚˆÓ ‹ÙÔ ÙÔ «Ì¤Á· ηٿÛÙȯÔÓ»(∫·ıÔÏÈÎfiÓ) ÂÎ ÙÔ˘ ÔÔ›Ô˘ ËÓÙÏÔ‡ÓÙÔ Î·È Ù· ¿ÏÏ· ηٿÛÙȯ· - ‚È‚Ï›· ÙÔ˘ ÂÌfiÚÔ˘29. ∆· ηٿÛÙȯ· ¿ÓÙˆ˜ ÂÙ¤ÏÔ˘Ó ˘fi ÓËÈÒ‰ËÓ Î·Ù¿ÛÙ·ÛÈÓ. µÂ‚·›ˆ˜ ÂÊ’ fiÛÔÓ ‰ÂÓ ¤¯ÔÌÂÓ ÂÌÂÚÈÛٷو̤ӷ˜ ËÁ¿˜ ÂÚ› ÙˆÓ ‚˘˙·ÓÙÈÓÒÓ ‚È‚Ï›ˆÓ, Ù· ˘Ê’ ËÌÒÓ ÏÂÁfiÌÂÓ· ‰‡Ó·Ù·È Ó· ·ÌÊÈÛ‚ËÙËıÔ‡Ó Î·È ˆ˜ ÁÂÈÙÓÈ¿˙ÔÓÙ· Ì ÂÈηۛ·˜, ı· ‹ÙÔ fï˜ -ηٿ ÙËÓ ÁÓÒÌËÓ ÌÔ˘- Ï›·Ó ·˘ÛÙËÚfi˜ Ô ÂÓ ÏfiÁˆ ÈÛ¯˘ÚÈÛÌfi˜ ÂÚ› «ÂÈηۛ·˜». ªÂ ÙËÓ ∞ÓÂÍ·ÚÙËÛ›·Ó (1828), ÂÙ¤ıË Î·È ÙÔ ı¤Ì· Ù˘ ·Ó¿Á΢ ¯Ú‹Ûˆ˜ ¶ÂÚ› ÙÔ˘ ‰ÈÏÔÁÚ·ÊÈÎÔ‡ Û˘ÛÙ‹Ì·ÙÔ˜ ÂȘ ÙÔ µ˘˙¿ÓÙÈÔÓ 11
ÏÔÁÈÛÙÈÎÒÓ ‚È‚Ï›ˆÓ ˘fi ÙÔ˘ ÓÂÔÛ˘ÛÙ¿ÙÔ˘ ∫Ú¿ÙÔ˘˜ Î·È ÙˆÓ ÂȯÂÈÚËÌ·ÙÈÒÓ, ‰ËÌÔÛȇıË ‰Â Î·È ‚È‚Ï›ÔÓ ÔÏ›ÁˆÓ ÛÂÏ›‰ˆÓ ÂÚ› ‰ÈÏÔÁÚ·Ê›·˜ ˘fi ™.∞. ¶·¿ ÙÈÙÏÔÊÔÚÔ‡ÌÂÓÔÓ «∂Á¯ÂÈÚ›‰ÈÔÓ ¢ÈÏÔÁÚ·Ê›·˜ (™‡ÓÙÔÌÔ˜ ¢È‰·Ûηϛ·), ÂÓ ∞ÈÁ›ÓË 1831»30. ∆Ô ¢ËÌfiÛÈÔÓ §ÔÁÈÛÙÈÎfiÓ ‰Â ÂÙ‹ÚÂÈ Ô ¤¯ˆÓ ÙËÓ Â˘ı‡ÓËÓ Ù˘ √ÈÎÔÓÔÌ›·˜ «¶Úfi‚Ô˘ÏÔ˜ Ù˘ √ÈÎÔÓÔÌ›·˜». √‡ÙÔ˜ ˘Â‚ÔËı›ÙÔ ÂȘ ÙÔ ¤ÚÁÔÓ ÙÔ˘ ˘fi ‰‡Ô ÂÙ¤ÚˆÓ ÌÂÏÒÓ ÙÔ˘ ¢ËÌÔÛ›Ô˘ §ÔÁÈÛÙÈÎÔ‡. √ ¶Úfi‚Ô˘ÏÔ˜ ›¯Â ÙÔ Î·ı‹ÎÔÓ Î·È ÙËÓ Â˘ı‡ÓËÓ Ù˘ ÙËÚ‹Ûˆ˜ ÙˆÓ ÏÔÁ·ÚÈ·ÛÌÒÓ Î·È Ù˘ ÎÏÂȉfi˜ ÙÔ˘ ∆·Ì›Ԣ fiÌÔ˘ Î·È Ì ÙËÓ Ù‹ÚËÛÈÓ ÙˆÓ ÏÔÁÈÛÙÈÎÒÓ ‚È‚Ï›ˆÓ Ù˘ ÃÚËÌ·ÙÈÛÙÈ΋˜ ∆Ú·¤˙˘31. ∏ ËÁÂÛ›· Ù˘ ∆Ú·¤˙˘ ÂÂÊÔÚÙ›ÛıË ÚÔÛˆÚÈÓÒ˜ Î·È Ì ÙÔÓ ¯ÂÈÚÈÛÌfiÓ ÙÔ˘ ¯Ú¤Ô˘˜ ÙÔ˘ ÀÔ˘ÚÁ›Ԣ √ÈÎÔÓÔÌÈÎÒÓ (¢È¿Ù·ÁÌ· ÂÓ ∞ÈÁ›ÓË Ù˘ 7˘ √ÎÙˆ‚Ú›Ô˘ 1828 ÙÔ˘ ∫˘‚ÂÚÓ‹ÙÔ˘ πˆ¿ÓÓÔ˘ ∞. ∫·Ô‰ÈÛÙÚ›Ô˘ ˘ÔÁÂÁÚ·Ì̤ÓÔ˘ ˘fi ÙÔ˘ °Ú·ÌÌ·Ù¤ˆ˜ Ù˘ ∂ÈÎÚ¿ÙÂÈ·˜ ™˘Ú›‰ˆÓÔ˜ ∆ÚÈÎÔ‡Ë). √ ¶Úfi‚Ô˘ÏÔ˜ ÂÙ‹ÚÂÈ ÙÚÈÒÓ ÂȉÒÓ ‚È‚Ï›·, ÌÂÙ¿ ÙˆÓ Û˘ÓÂÚÁ·ÙÒÓ ÙÔ˘, ÂÓ ÙˆÓ ÔÔ›ˆÓ ‹ÙÔ Î·È ÙÔ ‚È‚Ï›ÔÓ Ù˘ ‰ÈÏÔÁÚ·Ê›·˜32.
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1. Cambridge Economic History of Europe ed. Cambridge at the University Press, 1965 Vol. III ÛÂÏ. ÛÂÏ. 104, 109. 2. √ Melis ÏËÓ ÙÔ˘ Barbarigo ·Ó·Ê¤ÚÂÙ·È Î·È ÂȘ ÙÔÓ Fratesna So- ranzo (1408) ÂȘ ÙÔ ÌÓËÌÂÈ҉˜ ‰ÈÂÚ¢ÓËÙÈÎfiÓ ¤ÚÁˆÓ ÙÔ˘ “Doc- umenti per la Storia Economica” Secoli XIII-XVI doc. 137 Î·È 138 ed. Leo S. Olscki 1972 ÛÂÏ. 73) Û¯ÂÙÈÎÒ˜ Ì ÙËÓ ˘’ ·˘ÙÔ‡ Ù‹ÚËÛÈÓ ÙÔ˘ ∫·ıÔÏÈÎÔ‡, ˆ˜ ›Û˘ Î·È ÂȘ ÙÔ˘˜ Giustiniani Î·È Badoer. ∂›Û˘ ÂȘ ÙËÓ ÛÂÏ›‰· 480 ÙÔ˘ ȉ›Ô˘ ¤ÚÁÔ˘ ÙÔ˘ Ô ªelis ·ÚÔ˘ÛÈ¿˙ÂÈ ÏÔÁ·ÚÈ·ÛÌfiÓ ÂÈÛ·ÁˆÁ‹˜ - ÂÍ·ÁˆÁ‹˜ ∫·ıÔÏÈÎÔ‡ Î·È ËÌÂÚÔÏÔÁ›Ô˘ ·Ó·ÊÔÚ¿˜ ηıËÌÂÚÈÓÒÓ Ú¿ÍˆÓ. ∂Ș ÙËÓ ÛÂÏ›‰· 382 Ô Melis ·Ó·Ê¤ÚÂÙ·È Î·È ÂȘ ¿ÁÓˆÛÙÔÓ Âȯ›ÚËÛÈÓ ÂÓ 12 §¿˙·ÚÔ˜ £. ÃÔ˘Ì·Ó›‰Ë˜
™È¤ÓË (1277-1282) ·ÚÔ˘ÛÈ¿˙ˆÓ ‚È‚Ï›ÔÓ Ù˘ ¯ÚÂÒÛˆ˜ Î·È ÈÛÙÒÛˆ˜ ÙÔ˘ Ù·Ì›Ԣ Ù˘, ÂȘ ‰Â ÙËÓ ÛÂÏ›‰· 414 Ô ·Ó·ÁÓÒÛÙ˘ ı· ‡ÚË ÙÚÂ¯Ô˘Ì¤ÓÔ˘˜ ÏÔÁ·ÚÈ·ÛÌÔ‡˜ ÂȘ ÊÈÔÚ›ÓÈ· Î·È ¿ÏÏ· ÓÔÌ›ÛÌ·Ù·. 3. Cambridge Economic History of Europe Vol. III ÛÂÏ. 109. ∆ËÓ Ã¿ÓÛ· ÙËÓ ÔÔ›·Ó ·Ó·Ê¤ÚÔÌÂÓ ÂÓÙ·‡ı·. ·ÂÙ¤ÏÔ˘Ó 206 fiÏÂȘ, ·È ÔÔ›·È Û˘Ó¯Ҙ ÂÂÎÙ›ÓÔÓÙÔ, Ê˘ÛÈο Î·È Ù· Ù›¯Ë ÙˆÓ. ªÂ ÙËÓ ÂͿψÛÈÓ Ù˘ ·ÓÒÏÔ˘˜, Ë ÔÔ›· ÂÛÙ·Ì¿ÙËÛÂ Î·È ÂȘ µÚ·ÍÂÌ‚Ô‡ÚÁÔÓ (1351) ˘ÂÓÔ̇ıËÛ·Ó Î·È ·È fiÏÂȘ Ù˘ ÿÓÛ·, ·È ÔÔ›·È ›¯ÔÓ Î·Ù·ÚÁ‹ÛË Ù· ÌÂٷ͇ ÙˆÓ ÙÂψÓÂȷο Ù¤ÏË ¯¿ÚÈÓ Ù˘ ÎÔÈÓ‹˜ ¢ËÌÂÚ›·˜ ÙˆÓ (R. Dollinger, The German Hansa (·ÁÁÏ. ÌÂÙ. London 1970, ÛÂÏ. ÛÂÏ. 55, 56), §. £. ÃÔ˘Ì·Ó›‰Ë˜, √ÈÎÔÓÔÌÈ΋ πÛÙÔÚ›· Î·È Ë ∂ͤÏÈÍȘ ÙˆÓ √ÈÎÔÓÔÌÈÎÒÓ £ÂˆÚÈÒÓ, ∞ı‹Ó·È 1980, ∆ÔÌ. ÂΉ. ¶··˙‹ÛË, ÛÂÏ. ÛÂÏ. 654, 655. 4.,5. Cambridge Economic History of Europe Vol. III, ÛÂÏ. ÛÂÏ. 104, 109. 6. ∞. Sapori, Studi di Storia Economica (Secoli XIII-XVI-XV) ed. G.C. Sansoni, Firenze 1955, ÛÂÏ. ÛÂÏ. 96, 572-592. 7. G. Luzzatto, Storia Economica d’ Italia. L’ Antichità, il Mediol- vo ed. Leonardo, Roma 1949, ÛÂÏ. 140. Cambridge Economic History of Europe, 1965 Vol. III, ÛÂÏ. 94. 8.,9. §.£.ÃÔ˘Ì·Ó›‰Ë˜, «√ÈÎÔÓÔÌÈ΋ πÛÙÔÚ›· Î·È Ë ∂ͤÏÈÍȘ ÙˆÓ √ÈÎÔÓÔÌÈÎÒÓ £ÂˆÚÈÒÓ», ∞ı‹Ó·È 1980, ÂΉ. ¶··˙‹ÛË, ∆ÔÌ. ∞ã, ÛÂÏ. ÛÂÏ. 46, 490. 10. G. Barbieri, Origini del capitalismo Lombardo ed. Giuffrè, Milano 1961 ¤Óı· ·Ó·Ê¤ÚÂÈ fiÙÈ ÌÂٷ͇ ÙˆÓ ÍÂÓÔ‰fi¯ˆÓ ‰ÈÂÎÚ›ıË Ô An- tonio de Alliate Î·È ÌÂٷ͇ ÙˆÓ ÓÔÌÈÎÒÓ Ô Bonaccorso de Alli- ate [(ÛÂÏ. 13) §.£. ÃÔ˘Ì·Ó›‰ËÓ op. cit. ÛÂÏ. 525]. 11. G. Borbieri, op. cit. ÛÂÏ. 51. 12. §.£.ÃÔ˘Ì·Ó›‰Ë˜, √ÈÎÔÓÔÌÈ΋ πÛÙÔÚ›· Î·È Ë ∂ͤÏÈÍȘ ÙˆÓ √ÈÎÔÓÔÌÈÎÒÓ £ÂˆÚÈÒÓ, ∞ı‹Ó·È 1980, ÂΉ. ¶··˙‹ÛË, ∆ÔÌ. ∞ã, ÛÂÏ. 224. ªÂٷ͇ ÙˆÓ ÎˆÏ˘ÔÌ¤ÓˆÓ (·ËÁÔÚÂ˘Ì¤ÓˆÓ) ‹Û·Ó, Ô ¶ÂÚ› ÙÔ˘ ‰ÈÏÔÁÚ·ÊÈÎÔ‡ Û˘ÛÙ‹Ì·ÙÔ˜ ÂȘ ÙÔ µ˘˙¿ÓÙÈÔÓ 13
Û›ÙÔ˜, Ô ¯Ú˘Ûfi˜, Ô ¿ÚÁ˘ÚÔ˜, ÙÔ ¤Ï·ÈÔÓ, Ô Ô›ÓÔ˜, ÙÔ ¿Ï·˜, ÔÈ È¯ı›˜, Ù· ˆ¿ (·˘Á¿), Ù· ÂÚÁ·Ï›·, ÂÎÙfi˜ Î·È ·Ó ˘‹Ú¯ÔÓ ÂÚÈÛÛ‡̷ٷ ÙÔ‡ÙˆÓ, ˆÚÈṲ̂ӷ ÂÓ‰‡Ì·Ù·, Î·È Ë ·ÓÂÂͤÚÁ·ÛÙÔ˜ ̤ٷͷ. ∂›Û˘, ·ËÁÔÚ‡ÂÙÔ Ë ÂÈÛ·ÁˆÁ‹ ˆÚÈÛÌ¤ÓˆÓ ÂȉÒÓ ‰˘Ó·Ì¤ÓˆÓ Ó· Û˘Ó·ÁˆÓÈÛıÔ‡Ó ÙËÓ ÂÁ¯ÒÚÈ·Ó ·Ú·ÁˆÁ‹Ó, ˆ˜ Ï.¯. Ô Û¿ˆÓ Ù˘ ª·ÛÛ·Ï›·˜. 13. A, Fanfani, Storia Economica ed. Principato-Milano-Messino, 1956, ÛÂÏ. 44. 14.,15. F. Melis, Aspetti di Storia Economica Medievale ed. Banco di Siena, 1962, ÛÂÏ. ÛÂÏ. 342, 346 Î.Â. TÔ giornale ·Ê‡ڷ ÂȘ ÙËÓ ‰ÈÏÔÁÚ·Ê›·Ó, Ë ÔÔ›· ÂÊ¢ڤıË Î·È ÂÊËÚÌfiÛıË ÙÔ ÚÒÙÔÓ ÂȘ ÙËÓ πÙ·Ï›·Ó, ηٿ ÙÔ Ù¤ÏÔ˜ ÙÔ˘ 13Ô˘ ·ÈÒÓÔ˜, ηÙfiÈÓ ÂȘ ÙËÓ °·ÏÏ›·Ó, Î·È Â›Ù· ÂȘ ‰È·ÊfiÚÔ˘˜ ¿ÏÏÔ˘˜ ¯ÒÚ·˜, ÚÔ ‰Â ÙÔ˘ ¤ÙÔ˘˜ 1453 ÂÓ ∞ÁÁÏ›·, ÔÌÔ‡ Ì ٷ˜ ÈÛÙˆÙÈο˜ ÂÈÛÙÔÏ¿˜, Û˘Ó·ÏÏ·ÁÌ·ÙÈο˜ Î·È ÙÔÈ·‡Ù·˜ ÂȘ ÙÔÓ ÎÔÌÈÛÙ‹Ó (Raymond de RÔÔver: Business, Banking and Economic ∆hought., ed. Chicago University Press ÛÂÏ. ÛÂÏ. 119 Î.Â.). ¶ÂÚ› ÙÔ˘ ÈÛÙÔÚÈÎÔ‡ Ù˘ ‰ÈÏÔÁÚ·Ê›·˜ ÂȘ Ù· ·Ó·ÊÂÚı¤ÓÙ· Û˘ÁÁÚ¿ÌÌ·Ù· ÙÔ˘ Federigo Melis ›Û˘ ÂȘ ÙÔ˘ ȉ›Ô˘: Giornale e Partita Doppia presso un Azienda Fiorentina (1403) ÂȘ Saggi di Economia Aziendale e So- ciale ÂȘ «Memoria di Cino Zappa», Milano 1961 Vol. III, ÛÂÏ. ÛÂÏ. 1457-1473. ∂›Û˘ Ô Melis ·Ó·Ê¤ÚÂÙ·È Î·È ÂÚ› ËÌÂÚÔÏÔÁ›Ô˘ ‰ÈÏÔÁÚ·Ê›·˜ ÙËÚÔ˘Ì¤ÓÔ˘ ˘fi Ù˘ ÂÙ·ÈÚ›·˜ Del Bene ÂÓ °ÂÓÔ‡Ë (1391), (F. Melis, Aspetti di Storia Economica Medievale ed. Banco di Siena, 1962, ÛÂÏ. ÛÂÏ. 428, 434), À. Re- nouard, Les hommes d’ affairs italiens… ÛÂÏ. 177, §.£. ÃÔ˘Ì·Ó›‰Ë, √ÈÎÔÓÔÌÈ΋ πÛÙÔÚ›· Î·È Ë ∂ͤÏÈÍȘ ÙˆÓ √ÈÎÔÓÔÌÈÎÒÓ £ÂˆÚÈÒÓ, ÂΉ. ¶··˙‹ÛË, ∞ı‹Ó·È 1980, ∆ÔÌ. ∞ã, ÛÂÏ. ÛÂÏ. 489-490). 16. Cambridge Economic History of Europe ed. Cambridge at the University Press, 1965 Vol. III ÛÂÏ. ÛÂÏ. 90. 17. F. Melis, Aspetti di Storia Economica Medievale ed. Banco di Siena, 1962, ÛÂÏ. 347. ∞. Fanfani, Un mercante del 300, ed. Giuf- frè, Milano 1935 (¶·Ú¿ÚÙËÌ· ÂȘ ∫ÂÊ. VII ÛÂÏ. ÛÂÏ. 65 Î.Â.). 14 §¿˙·ÚÔ˜ £. ÃÔ˘Ì·Ó›‰Ë˜
18,19 F. Melis, Ôp. cit. ·˘ÙfiıÈ, R. de Roover op. cit. ÛÂÏ. 177. 20. F. Melis, Aspetti di Storia Economica Medievale ed. Banco di Siena, 1962, ÛÂÏ. ÛÂÏ. 592, 596 Î.Â. 21. ∏ ÂÈÙ·Á‹ Â͉fiıË ÙÔ ÚÒÙÔÓ ÙÔ ¤ÙÔ˜ 1324 › ∆Ú·¤˙˘ Paraz- zone e Donato ÂÓ ¶›˙Ë (F. Melis, Note di Storia Banca Pizana nel trecento, Pisa 1950 ÛÂÏ. ÛÂÏ. 63 Î.Â.). 22. ∏ Û˘Ó·ÏÏ·ÁÌ·ÙÈ΋ ÂÊËÚÌfiÛıË, ηٿ ÙÔÓ Renouard, Èı·ÓfiÓ ÙÔ ÚÒÙÔÓ ÂÓ °ÂÓo‡Ë ÙÔ ¤ÙÔ˜ 1291 (Y. Renouard, op. cit. ÛÂÏ. 176). ¶ÂÚ› Ù˘ ÔÈÛıÔÁÚ·ÊË̤Ó˘ Û˘Ó·ÏÏ·ÁÌ·ÙÈ΋˜, ηْ ·Ú¯‹Ó, Û˘Ó¤‚·ÏÂÓ Ô De Rouver, Ô ÔÔ›Ô˜ ÙËÓ ÂÙÔÔı¤ÙËÛ ÙÔ ¤ÙÔ˜ 1520, Ô Melis fï˜ ·Ó·Î¿Ï˘„ÂÓ ÂȘ ÙÔ ∞گ›ÔÓ Ù˘ ÂÙ·ÈÚ›·˜ Datini ÂȘ Prato ÔÈÛıÔÁÚ·ÊË̤ÓËÓ Û˘Ó·ÏÏ·ÁÌ·ÙÈÎ‹Ó ÂΉÔıÂ›Û·Ó ÙÔ ¤ÙÔ˜ 1410 (F. Melis, Una girala cambiaria del 1410 nell’ Arehivio Datini di Prato ÂȘ Economia e Storia (Dir. A. Fanfani) Milano 1958 No2 ∆‡¯Ô˜ 4, ÂÏÏ. ÌÂÙ·ÊÚ. §.£. ÃÔ˘Ì·Ó›‰Ë, ªÈ· ÔÈÛıÔÁÚ·ÊË̤ÓË Û˘Ó·ÏÏ·ÁÌ·ÙÈ΋ ÙÔ˘ ¤ÙÔ˘˜ 1410 ¢ÚÂı›۷ ÂȘ ÙÔ ∞گ›ÔÓ Datini, §ÔÁÈÛÙ‹˜, ∆‡¯Ô˜ 79, ¡Ô¤Ì‚ÚÈÔ˜ 1960. 23. ∆Ô ÚÒÙÔÓ ÙÚ·Â˙ÈÎfiÓ ÁÚ·ÌÌ¿ÙÈÔÓ ÂÓÙÔ›˙ÂÈ Ô Fanfani ηٿ ÙÔ ‰Â‡ÙÂÚÔÓ ‹ÌÈÛ˘ ÙÔ˘ 13Ô˘ ·ÈÒÓÔ˜ ÂΉÔı¤ÓÙÔ˜ ˘fi ÙÔ˘ Francesco Datini (A. Fanfani, Storia Economica ÛÂÏ. 316). 24. F. Melis, Note di Storia …, ÛÂÏ. ÛÂÏ. 121, 142, 161. 25. Cambridge Economic History of Europe ed. Cambridge at the University Press, 1965 Vol. III ÛÂÏ. 44. 26. °. ¶··ÚÚËÁfiÔ˘ÏÔ˜, πÛÙÔÚ›· ÙÔ˘ ∂ÏÏËÓÈÎÔ‡ ŒıÓÔ˘˜, ∆ÔÌ. ¢ã, ÛÂÏ. 46, §.£.ÃÔ˘Ì·Ó›‰Ë˜, √ÈÎÔÓÔÌÈ΋ πÛÙÔÚ›· Î·È Ë ∂ͤÏÈÍȘ ÙˆÓ √ÈÎÔÓÔÌÈÎÒÓ £ÂˆÚÈÒÓ, ∞ı‹Ó·È 1980, ÂΉ. ¶··˙‹ÛË, ∆ÔÌ. µ2 ÛÂÏ. 170. 27. ∞.™. ¢·Ì·Ï¿˜, √ ÔÈÎÔÓÔÌÈÎfi˜ ‚›Ô˜ Ù˘ Ó‹ÛÔ˘ Ã›Ô˘, ∞ı‹Ó· 1998, ÙfiÌÔ˜ ¢ã, ÛÂÏ. 46. 28.,29. µ.º. º›ÏÈÔ˘, §ÔÁÈÛÙÈ΋ Î·È ÂÌÔÚÈΤ˜ ÛÔ˘‰¤˜ ÛÙËÓ ∂ÏÏ¿‰·, ηٿ ÙËÓ ÂÔ¯‹ Ù˘ ∆Ô˘ÚÎÔÎÚ·Ù›·˜ ̤¯ÚÈ Î·È ÙËÓ ›‰Ú˘ÛË Ù˘ ∞™√∂∂ «∞گ›ÔÓ √ÈÎÔÓÔÌÈ΋˜ πÛÙÔÚ›·˜», ∆ÔÌ.V, No12, 1994, ¶ÂÚ› ÙÔ˘ ‰ÈÏÔÁÚ·ÊÈÎÔ‡ Û˘ÛÙ‹Ì·ÙÔ˜ ÂȘ ÙÔ µ˘˙¿ÓÙÈÔÓ 15
ÛÂÏ. ÛÂÏ. 132-135. 30. §.£.ÃÔ˘Ì·Ó›‰Ë˜, √ÈÎÔÓÔÌÈ΋ πÛÙÔÚ›· Î·È Ë ∂ͤÏÈÍȘ ÙˆÓ √ÈÎÔÓÔÌÈÎÒÓ £ÂˆÚÈÒÓ, ∞ı‹Ó·È 1981, ∆fiÌÔ˜ 2µ, ÂΉ. ∫·Ú·ÌÂÚfiÔ˘ÏÔ˜, ÛÂÏ. 497. 31. §.£.ÃÔ˘Ì·Ó›‰Ë˜, ¶ÂÚ› Ù˘ ˘fi ÙÔ˘ πˆ¿ÓÓÔ˘ ∫·Ô‰ÈÛÙÚ›Ô˘ È‰Ú˘ı›Û˘ ∂ıÓÈ΋˜ ÃÚËÌ·ÙÈÛÙÈ΋˜ ∆Ú·¤˙˘, ¶·ÚÓ·Ûfi˜ (·Ó¿Ù˘ÔÓ) ∆fiÌÔ˜ §˜, 1994, ÛÂÏ. 21. 32. §.£. ÃÔ˘Ì·Ó›‰Ë˜, ∞˘ÙfiıÈ, µ. º›ÏÈÔ˜, ∞˘ÙfiıÈ.
µπµ§π√°ƒ∞ºπ∞
ÕÌ·ÓÙÔ˜ ∫. (1941), ¶ÂÚ› ∂ÌÌ·ÓÔ˘‹Ï °Ï˘Ù˙Ô˘Ó›Ô˘, ∆· ÁÚ¿ÌÌ·Ù· ÂȘ ÙËÓ Ã›ÔÓ Î·Ù¿ ÙËÓ ∆Ô˘ÚÎÔÎÚ·Ù›·Ó, ¶ÂÈڷȇ˜. ∂›Û˘ ÙÔ˘ ›‰ÈÔ˘ Ë §ÔÁ·ÚÈ·ÛÙÈ΋ ÙÔ˘ °Ï˘Ù˙Ô‡ÓË ÂȘ «∏ÌÂÚÔÏfiÁÈÔÓ Ù˘ ªÂÁ¿Ï˘ ∂ÏÏ¿‰Ô˜», 1934 ÛÂÏ. ÛÂÏ. 179-184. Cambridge Economic History of Europe (1965), ed. Cambridge at the University Press, Cambridge, Vol. III. Fanfani, A (1955), Storia Economica, ed. Principato Milano-Messina. Heers, J. (1963, 1970), L’ Occident au XIV et ÃV siècles. Aspects Économiques et Sociaux, ed. Presses Universitaires France, Paris. Littleton A.G. - Yamey B.S. (1956), Studies ni the history of Accounting, London. Luzzatto, G. (1949), Storia Economica d’ Italia, l’ Antichità, il Medivero ed. Leonardo, Roma. Melis, F. (1951), Note di Storia della Banca Pisana nel Trecento, Pisa. Melis, F. (1950), Storia della Ragnoneria, Bologna. Melis, F. (1962), Aspetti di Stonia Economica Medioevale, ed. Banca di Siena, Siena. Melis, F. (1958), Una girata cambiaria del 1410 nell’ Archivio Datini di Pra- to, «Economia e Storia» No4 (ÂÏÏ. ÌÂÙ. §.£. ÃÔ˘Ì·Ó›‰Ë˜) ª›· 16 §¿˙·ÚÔ˜ £. ÃÔ˘Ì·Ó›‰Ë˜
ÔÈÛıÔÁÚ·ÊË̤ÓË Û˘Ó·ÏÏ·ÁÌ·ÙÈ΋ ¢ÚÂı›۷ ÂȘ ÙÔ ∞گ›ÔÓ Datini di Prato, §ÔÁÈÛÙ‹˜ ∆‡¯Ô˜ 79, ¡Ô¤Ì‚ÚÈÔ˜ 1960. ¶··ÚËÁfiÔ˘ÏÔ˜ ∫. (1871), πÛÙÔÚ›· ÙÔ˘ ∂ÏÏËÓÈÎÔ‡ ŒıÓÔ˘˜, ∆fiÌÔ˜ ¢ã ÂÓ ∞ı‹Ó·È˜. Peragallo, E (1981): Closing Procedures in the 15th Century Ledger Ja- chomo Badoer, a Venetian Merchant «The Accounting Re- view», July, ÛÂÏ. 587-595. Peragallo, E (1983): Development of the Double - Entry in the 15th Cen- tury Ledger. of Jachomo Badoer, a Venetian Merchant «The Accounting Review», January, Vol. III No1, ÛÂÏ. ÛÂÏ. 98-102. Peragallo, E (1988): The Ledger of Jachomo Badoer: Constantinople Sep- tember 2 1436 to February 26, 1440 «The Accounting Re- view» Vol. IV No4 ÛÂÏ. ÛÂÏ. 881-892. ^ Renouard Y. (1949-1968) Les Hommes d’ Alfaires Italiens au Majen Age ed. Armand Colin, Paris. Roover R. de (1956), Strodies in the History of Accounting, Business Bunking and Economic Thought, ed. Chicago University, Press, Chicago. Sapori, A. (1955), Studi di Stonia Economica secoli XIII-XIV-XV) Vol- ume primo, ed. Sansoni, Firenze. º›ÏÈÔ˜, º.µ. (1994), §ÔÁÈÛÙÈ΋ Î·È ÂÌÔÚÈΤ˜ ÛÔ˘‰¤˜ ÛÙËÓ ∂ÏÏ¿‰· ηٿ ÙËÓ ÂÔ¯‹ Ù˘ ∆Ô˘ÚÎÔÎÚ·Ù›·˜ ̤¯ÚÈ Î·È ÙËÓ ›‰Ú˘ÛË Ù˘ ∞™√∂∂, «∞گ›ÔÓ √ÈÎÔÓÔÌÈ΋˜ πÛÙÔÚ›·˜», ∆ÔÌ.V No1- 2, 1994, ÛÂÏ. ÛÂÏ. 117-149. ÃÔ˘Ì·Ó›‰Ë˜, §.£. (1990), √ÈÎÔÓÔÌÈ΋ πÛÙÔÚ›· Î·È Ë ∂ͤÏÈÍȘ ÙˆÓ √ÈÎÔÓÔÌÈÎÒÓ £ÂˆÚÈÒÓ, ÂΉ. ¶··˙‹ÛË, ∞ı‹Ó·È, ∆ÔÌ. ∞ Î·È µ2. ÃÔ˘Ì·Ó›‰Ë˜, §.£. (1990), √ÈÎÔÓÔÌÈ΋ πÛÙÔÚ›· Ù˘ ∂ÏÏ¿‰Ô˜, ∆ÔÌ. ∞ã- µ, ÂΉfiÛÂȘ ¶··˙‹ÛË, ∞ı‹Ó·È. Aگ›ÔÓ OÈÎÔÓÔÌÈ΋˜ IÛÙÔÚ›·˜ / Archives of Economic History, XV/2/2003 17
UNCERTAINTY, TAXATION AND ENTREPRENEURIAL ENTRY AUKE R. LEEN University of Leiden
Abstract
In what way do higher taxes and uncertainty influence the decision to become an entre- preneur? In other words, “What tax system suits entrepreneurial entry in the market process best?” The paper answers the question from the Austrian perspective. The perspective is to be contrasted with the mainstream neoclassical perspective. If the market -as the Austrians do say- is a process of discovery, the first effect of a tax system is not its effect on the rela- tive preferability for the decision-maker of already-perceived alternative courses of action. The effect we have to take into account is, first and foremost, the possibility that the tax may have significant impact upon the very perception by the prospective taxpayer of what array of opportunities are available for his choice. This view goes against the mainstream view that higher taxes could serve as an insurance against the greater risk in self-employment as com- pared to that in wage employment. In terms of policy implications, tax relief efforts aimed at small businesses for sure do foster entrepreunerial entry. Raising taxes, however, even with full loss recovery, might be a risky “strategy” to increase entrepreneurial entry. JEL classification: B53, H21, M13. Keywords: entrepreneurship, uncertainty, taxation.
1. Introduction
Ever since the article that started it all of Domar and Musgrave: Propor- tional Income Taxation and Risk-Taking (1944; compare for more recent updates and theoretical refinements, e.g., Feldstein, 1969; Stiglitz, 1969; Kanbur, 1981; Kihlstrom and Laffont, 1983; and Gentry and Hubbard, 2000) about the influence of taxation on investment in risky ventures and entrepreneurial entry, we do have that surprising and intriguing result: the higher the tax rates are, the greater is the amount of risk an entrepreneur is willing to take and hence entrepreneurial entry will be (that is the deci- sion of wage-and-salary employees to become self-employed). The moti- 18 Auke R. Leen vation of this now widely accepted proposition by professional economists (Feldstein, 1969, p. 755, cp. Blau, 1987, p. 464) goes as follows. If losses can be offset, both the yield (defined as the mean portfolio return anticipated when all possible returns are considered) and the risk (defined as the sum of antici- pated negative incomes weighted by their probabilities) of the investment have been reduced by the rate of the tax. (Hence: yield = gain (defined as the sum of anticipated positive incomes weighted by their probabilities) – risk). The extent to which loss offset is possible in actual practice depends of course on the offset provisions in the tax law and upon the availability of other in- come. With full loss offset, the return per unit of risk-taking remains un- changed. In other words, the government assumes part of the risk as well as of the yield. In a sense the government appoints itself as a business partner to the entrepreneur. Though the total (society’s) risk remains the same, the en- trepreneur’s (individual) risk has been reduced. But the entrepreneur’s in- come has been reduced too. To restore his income, he will take higher yield- ing and more risky investments. If this result is extended beyond a portfolio choice into an occupational choice framework (see, e.g., Kanbur, 1981): en- trepreneurial entry will increase too. A result confirmed as recently as 2000 by Bruce: higher relative tax rates in self-employment were found to increase the rate of entry. Or as said by Bruce in 2002, “higher tax rates on income from self-employment do not increase, and might actually reduce, the proba- bility that an individual will exit self-employment.” Bruce (2000, 2002) also gives a second reason given in the literature for the result just-discussed. Motives of tax avoidance and evasion are at the heart of this reason. Higher tax rates on self-employment income translate into greater rewards form avoidance and evasion. In other words, higher marginal tax rates seem to encourage self-employment relative to wage- employment. Self-employment offers greater opportunities to avoid or evade taxes than wage-employment does (Parker, 1996, p. 472). This is confirmed by the fact that the voluntary reporting percentage for wages and salaries (subject to third-party reporting and withholding) is over 99 percent for fillers, while the percentage for all other income is 80 percent (Joulfaian and Rider, 1998, p. 675). Hence reducing those rewards may even lead to reduced entrepreneurial entry. “If some entrepreneurs are ac- tually creative tax-evaders, then reducing their marginal tax rates could en- courage them to close their ‘businesses’” (Bruce, 2002, p. 8). Uncertainty, taxation and entrepreneurial entry 19
It appears that the just-cited results go against what Frederic Bastiat (a predecessor of modern-Austrian economics) and Ludwig von Mises (the founder modern-Austrian economics) taught us. Bastiat said us to “accus- tom ourselves […] not to judge things solely by what is seen, but rather by what is not seen” ([1850], 1964, p. 9). Therefore, as far as taxes are con- cerned, he wrote: “You compare the nation to a parched piece of land and the tax to a life giving rain. So be it. But you should also ask yourself where this rain comes from, and whether it is not precisely the tax that draws the moisture from the soil and dries it up” (o.c., p. 8). And Mises, [1949], 1966, p. 741 said, “This metamorphosis of taxes into weapons of destruction is the mark of present-day public finance.” In this paper we look, in the tradition of Bastiat and Mises, at tax systems with regard to the ultimate unseen: we even do not know what we do not know. In other words, we examine a tax system that fits the market econo- my. This since the essence of the market economy -from the perspective of the modern Austrians1- is that it is a system of competitive-entrepreneurial discovery. In other words, what characterizes the market economy is com- petition, what drives the market is entrepreneurship, and what constitutes the steps in the market process are discoveries. In the market process we discover new ends and means. Accordingly, a tax system can be assessed with respect to the ability to promote creative acts of entrepreneurship. And we conclude that to increase taxes and hence to buffer uncertainty is not the one-way bet it seems to be as far as entrepreneurial entry goes. The central thesis of this paper, to be explained more fully later, is the fol- lowing. The risk Musgrave and Domar do speak about (and modern neoclas- sical economists do too) is the risk of a known alternative. Indeed, if that is the situation, to look at relative preferability is the right (economic) thing to do. We, e.g., look at the changing relative gains of higher taxes on committing tax fraud for wage earners as compared to the self-employed; and then, in- deed, the stated results do follow (see, e.g., Blau, 1987, and Bruce, 2000). However, if it is utter ignorance (uncertainty) we are speaking about, and that is the situation for the entrepreneur in his day-to-day practice, taxation robs the entrepreneur of the incentive to come up with the promising investments (with or without a high risk) in the first place. In other words, for Austrian eco- nomics fundamental uncertainty is of the essence of the situation the entre- preneur faces. His situation is not one of uncertainty over given alternatives. 20 Auke R. Leen
The entrepreneur has, first of all, to come up with those alternatives. He has to come up with a framework of ends and means (cp. Kirzner, 1973, pp. 82- 84). Afterwards he can assess the riskyness of the ends and means. Kanbur (1981, p. 179), in his neoclassical framework, also does come up with an element of discrete, non-marginal choice as of the essence of entre- preneurship. As far as his emphasis is on the real choice element in entre- preneurship there is indeed not “a little bit” more in entrepreneurial activity and he is correct. He places his analysis, however, in a general equilibrium framework: the choice is between existing “alternative activities that differ in their risk characteristics.” Riskiness of self-employement (since it is unob- servable), in order to be modeled in a neoclassical model, needs a proxy. Parker, e.g., uses as a proxy “the turbulence of industrial relations, as meas- ured by the number of strikes” (1996, p. 465). To do this is of course, by def- inition, out of the question for the modern-Austrian. Since the general equi- librium framework lacks fundamental error and hence the unknown choices open to the entrepreneur. Which is of the essence of Austrian economics. The influence, also, of taxation on risk is a different one for each of these two problems: known uncertainty of “given” means and ends versus fun- damental uncertainty as far as what are the means and ends in the first place. Neoclassical economics hints at the influence of taxation in regard to the first form of risk. Austrian economics hints at the influence of taxation in regard to the second form of risk. Fundamental ignorance and hence an ultimate error stands against a situation of given alternatives involving risk (of which we do know the probability distribution of incomes attached to each alternative). For the Austrian, entrepreneurship is defined as the very perception of the ends-means framework within which allocation and econ- omizing is to take place (Kirzner, 1973, p.33). For the neoclassical it is de- fined as combining individual-specific ability with an up-front investment to generate an uncertain return (Gentry and Hubbard, 2000, p. 283).
2. The core of Austrian economics
Let us first expend a little bit on the intricacies of the core of Austrian economics. In 1871 Carl Menger's value theory turned the value theory of the classical economists upside down. The classical (Ricardian) theory held Uncertainty, taxation and entrepreneurial entry 21 that cost of production determines the normal value of consumption goods. In contrast, Menger's theory held that the value of consumption goods ul- timately determines the cost of production. Value is an expression of judge- ments concerning future usefulness in meeting consumer wants. Hence does follow one of the Austrian fundamentals of taxation, “No tax can be shifted forward” (Rothbard, 1970, p. 88). Prices, as we just said, are never determined by costs of production; the reverse is true. Think of it. There is no reason to expect the producer to wait on, e.g., a general sales tax to in- crease his prices if he could have done so before. Since the selling price is already set at a “maximum”; a rise in costs, ic. an imposed general sales tax, cannot raise the price any further. The price is determined by the total stock in existence and the demand schedule for it on the market. Hence the fact that the sticker price of a product does show a certain amount of sales tax does not prove that it is shifted forward towards the consumer. The price for the producer for a good on the market is not the market price mi- nus the sales tax. It is just that market price. The price minus the sales tax the producer gets might well have been reduced to allow for the payment of taxes. So it makes the income the producer receives less. Hence a sales tax is an income tax on the production factors (Rothbard, 1970, pp. 88-93). Israel Kirzner describes modern Austrianism as an authentic extension of Menger's older static subjectivism: a consequent dynamic subjectivism. In modern Austrianism, the two central figures are Ludwig von Mises and Friedrich Hayek. Both authors focus on market adjustment processes. Kirzner, building his theory as Mises and Hayek did, believes that one of the greatest failures of neoclassical (equilibrium) analysis is that it assumes equi- librium is actually brought about. The real problem for modern Austrians is to describe the possible realization of an equilibrium as the result of “the sys- tematic way in which plan revisions are made as a consequence of the dis- appointment of earlier plans” (Kirzner, 1962, p. 381). Mises and Hayek made it possible to describe adjustment as a systematic sequence of decisions. Mises's extension of subjectivism was to describe the individual decision unit not only as maximizing, but also as finding out the relevant ends means relationship. This opened the way for incorporating learning into our understanding of market processes. Hayek's extension of subjectivism was to describe the process as one of learning by discovery. Endogenous change in the ends-means relationship -says Kirzner- is possi- 22 Auke R. Leen ble with the entre-preneurial element in each individual market participant: alertness. Alertness is “the propensity [...] toward fresh goals and the dis- covery of hitherto unknown resources” (1973, p. 34). A disequilibrium sit- uation points to market ignorance. From it emerge profitable opportuni- ties that are exploited by alertness. Alertness gives a more realistic image of human action (and hence real choice) and makes possible the description of the market as a unified discovery process. “[The] ‘alertness’ view of the entrepreneurial role rejects the thesis that if we attribute genuine novelty to the entrepreneur, we must necessarily treat entrepreneurially generated market events as not related to earlier market events in any systematic way. The genuine novelty [...] attribute[d] to the entrepreneur consists in his spontaneous discovery of the opportunities marked out by earlier mar- ket conditions (or by future market conditions as they would be in the ab- sence of his own actions)” […] “[These] entrepreneurial discoveries are the steps through which any possible tendency toward market equilibrium must proceed” (Kirzner, 1985, pp. 11-12).
3. Two views on risk: the un- and counter expected
At this point we do answer our core question: What influence does the tax system has on entrepreneurial entry (occupational choice) and hence the market’s competitive-entrepreneurial discovery process? If the market is a process of discovery, the first effect of a tax system is not it’s effect on “the relative preferability for the decision maker of already-perceived alternative courses of action” (Kirzner, 1985, p. 94) as the neoclassical tells us. No, the effect we have to take into account is “the possibility that the tax may have, perhaps, significant impact upon the very perception by the prospective tax- payer of what array of opportunities are available for his choice” (o.c., p. 94). To answer our question, we do have to distinguish between the truly un- expected and the counter-expected. For Austrians uncertainty (risk) is first and foremost illustrated in the appearance of something completely unex- pected. “[T]he situation holds unknown possibilities unconstrained by known constraints. It is the entrepreneur’s awareness of the open-ended- ness of the decision context that appears to stimulate the qualities of self- reliance, initiative, and discovery” (Kirzner, 1985, p. 109). For the neo- Uncertainty, taxation and entrepreneurial entry 23 classical, however, only counter-expected things do happen. He thought to be 99 percent sure the sun would shine tomorrow. But the counter-expect- ed did happen: it rained! In mean-stream economics the entrepreneur is “the ultimate bearer of irreducible, noninsurable risk” (Kanbur, 1982, p. 2; cp. Kihlstrom and Laffont, 1983, p. 163, who describe the entrepreneur as someone who “receives the random profits of the firm he creates”). For the Austrian, however, the entrepreneur spots something, we even did not know it could happen at all. This is something completely different as to speak of an uninsured idiosyncratic risk. It also means, and that is the crux of our paper, that first and for all, an error (utter ignorance) in a market economy does unveil itself by showing up as an opportunity for monetary profit. So it looks as if it is the entrepreneur -to stimulate his discovery process (for that is what the entrepreneur does by correcting genuine errors stimulated by monetary profit)- we do have to focus on. If this is the case, we can say that any form of taxation that lowers prospective profits (the way an error reveals itself and that provides the incentive that inspires en- trepreneurial discovery of unnoticed opportunities) goes against the entre- peneurial process of discovery the market is.2 Which, as just-said, is the bread and butter of the producer-entrepreneur. This is our first reason to exempt the producer from any form of taxation. It is an argument against all corporate income taxes. A second reason to exclude the entrepreneur from taxation is that de- mand is not the desire of the consumer for a hypothetical product not yet produced. “[T]he demand that is expressed in the demand curve for a prod- uct means the quantities of it that consumers will be prepared to buy, at given prices, when offered the opportunity of doing so” (Kirzner, 1973, p. 178). Consumer sovereignty means that production patterns are dictated by the pattern of consumer demand. To be more specific “production deci- sions are determined by entrepreneurial anticipation of the patterns of de- mand that will be evoked by alternative production plans” (o.c. p. 176). So if the distortions of taxation -that is the impact on the discovery process- should be minimized, taxes should no be levied on the entrepreneur. Since he is the first, the conditio sine qua non, to come up with something new (correcting an error) in the causal market process. The third reason not to tax entrepreneurs goes as follows. If it is entre- preneurship we do focus on -so (as we just-said) the producer-entrepreneur 24 Auke R. Leen is central- profits have to be as visible and as promising as possible. Entre- preneurship has to be stimulated. Entrepreneurship involves fundamental uncertainty in general but also, and of particular relevance of here, uncer- tainty as far as the complexity and instability of the tax code goes: legisla- tive changes and tax court rulings. [T]he alert entrepreneur, discovering what seems to be an attractive opportunity, may have considerable misgiv- ings [uncertainty] concerning the venture” (Kirzner, 1973, p. 78). [F]rom the point of view of the prospective entrepreneur the profit opportunity is, with al its uncertainty, there” (o.c., p. 83). Often, because of either the sheer size or instability in the tax code, it is impossible to predict (there is funda- mental uncertainty) the tax consequences of a particular activity. This un- certainty leads to a loosening of the entrepreneurial grip on pure profit. This since profits or loses arising from tax changes, by a fortunate or unfortunate change in the tax system, do appear after the entrepreneur has taken up his position, A potential and in fact superior vision may be highly stifled. We do remove much of the incentive -to “purposeful alertness, the alert pur- posefulness” (Kirzner, 1999a, p. 39)- for paying attention to the unknown. Hence a tax system has to be as simple and predictable as possible. Fourth, Austrians emphasize the division of knowledge and its growth. Entrepreneurial opportunities tend to appear within the context of a spe- cific time and place. So -after Hayek (the Nobel Memorial Price in Eco- nomics winner in 1974)- a decentralized economy is the place to look at. It allows individuals to act on their entrepreneurial insights, and rewards them for doing so. The institutional setting of the market is especially fitted to stimulate discovery. It produces an environment where entrepreneurship is stimulated. And since entrepreneurial insights lay also the foundation for additional entrepreneurial insights the growth process of the economy is sustained. The market system encourages the full use of (decentralized) hu- man knowledge. There is no efficient non-market, e.g., governmental, re- source allocation. This was the insight the Austrians tried to bring to the fore in the socialist-calculation debate that raged in the interwar period. A debate that began with the question, “Is an efficient non-market resource allocation possible?” For the Austrian, market based prices are necessary to signal scarcity, to transmit knowledge, and to stimulate discovery. Hence the government cannot be trusted to do this job for society, that is, guiding the discovery process, by changing the relative preferability of out- Uncertainty, taxation and entrepreneurial entry 25 comes and means of production. And as Mises concludes: “Inasmuch as money prices of the means of production can be determined only in a so- cial order in which they are privately owned, the proof of the impractica- bility of socialism necessarily follows. […] [T]his proof is certainly the most important discovery made by economic theory” (1981, p. 15). A dis- covery (that is using decentralized in stead of centralized knowledge) a con- sumption tax tries to live up to. Hence, a simple uniform consumption tax system comes up as a logical corollary. There simply is no efficient gov- ernmental resource allocation by means of taxation.
4. Summary and policy conclusions
If it is sparking interest we are looking at (that is not changing relative at- tractiveness), we do -in fact- focus on the effects of taxing pure (unknown) entrepreneurial profit. This instead of mainstream neoclassical analysis that focuses on changing the (known) relative preferability of the options the pro- ducer-entrepreneur faces. Pure profit is a sum that cannot be described as necessary for the production of the item sold; the producer has already re- covered all his expenses (opportunity costs). But alertly noting hitherto un- noticed opportunities depend on the possibility of the emergence of pure profit. In other words, worthwhile opportunities may simply not be noticed in the absence of the possibility of pure profit. For the Austrian, this is a valid description of the situation the entrepreneur faces. Hence taxing pure profit should be looked at with suspicion at the least. As Kirzner says, progressive taxation changes an open-ended world into a closed one (1999b, p.109). If, in order to have a profit, it were luck we are counting on, no incentive what- soever would be necessary. Neither are profits wholly, as Frank Knight would say, the uncertainty-bred differences between the anticipated value of re- source services and their actual value” (Kirzner, 1973, p. 82). What we are looking at is a potentially attractive outcome (on the basis of active, alert, searching entrepreneurial activity) in an open-ended world: an unknown pos- sibility unconstrained by known constraints. “The most impressive aspect of the market system is the tendency for [...] opportunities to be discovered” (Kirzner, 1985, p. 30). Prices expressed in money show price discrepancies. Through the possibility of monetary profits, prices stimulate the discovery of 26 Auke R. Leen valuable concrete information. And it is precisely the institutional setting of the market economy that translates utter error into prospective net gain. It is a social setting in which people are continuously pressed to improve. The study of risk taking, taxation, and entrepreneurship has often been motivated from the point of view of policy. To sum it all up, for the neo- classical economist the effects of progressive taxation on risk taking are positive if risk aversion is greater than unity. “[H]igher marginal tax rates seem to encourage self-employment relative to paid employment” (Park- er, 1996, p. 472; cp. Richter, 1960, p. 164). In the neighborhood of risk neu- trality, however, it reduces risk taking (Kanbur, 1997, p. 790). And since “[r]isk and income move together because, ceteris paribus, greater income is a reward for bearing greater risk” (Parker, 1996, p.462), the pattern of income distribution in a society reflects, in part, the pattern of risk taking in occupational choice (Friedman, 1953, p. 278). If so, however, the neo- classical economist sees a policy conflict (all depending on the assumptions about the risk attitude of the society in question) between the reduction of income inequality in society (by means of progressive taxation), the en- couragement of risk-taking (entrepreneurship) and the growth in national income. We can sum it up in the words of Kanbur, 1982, p. 19, who also does not see any general conflict between the stated objectives. Since, “the conflict only arises in particular cases and in particular ways. Theory has to provide models that illustrate these cases, and empirical analysis has to pro- nounce on the possible net effect of the different forces.” But the conflict, however illusory as Kanbur says it is, does only exist if the entrepreneur is seen as a risk taker per se. But “it should be clear that entrepreneurship as we have discussed it in no way depends on any specific attitude toward un- certainty-bearing on the part of the decision-makers” (Kirzner, 1973, p.78). If the entrepreneur is correcting fundamental errors, as the Austrians do say, the conflict vanishes. We are looking “for entrepreneurial alertness and for its effect upon the continued availability of perceived opportunities for pure profit” (o.c., p. 79). Also, though it is an empirical question as to whether what preferences for risk do exist in the different countries of this world in practice (cp. Feldstein, 1969, p. 763, who speaks of the necessity “of the exploration of a variety of restricted but plausible models”), the Austrian–based theoretical analysis does warn us that any general claim about the effects of taxation on inequality and growth of income should be Uncertainty, taxation and entrepreneurial entry 27 treated with caution. This because they do leave out the most important as- set of the market economy: entrepreneurial alertness. And again, if the Austrian perspective is the way to look at entrepreneur- ship, the remark made by, e.g., Kandur that “the [neoclassical] model leaves out an analysis of why entrepreneurship is beneficial in the long-run is with- out sense.” In other words, he says, “there is no modeling of what must be presumed to be a basic tenet of the conventional wisdom, in terms of the ‘dy- namism’ of an economy with a greater degree of entrepreneurship” (1982, pp. 19-20). See also the question asked by Richter: “‘Should’ risk taking be encouraged? […] [W]hat is desirable about encouraging ‘risk’ taking? In- deed, why should not society’s utility function register abhorrence to ‘risk’ as much as do those of most individuals?” (1960, p. 166). Compare what Stiglitz, 1969, p. 279 says: “Even if risk-taking is increased by a given type of tax, it is not clear that such a tax should be adopted: after all, risk-taking is not an end itself.” Or to give a last example of a question posed inside a neoclassi- cal market framework: “[D]oes market equilibrium have too many or too few entrepreneurs?” (Kanbur, 1981, p. 179). For the Austrian, however, it is all very clear. The correction of fundamental errors is a one-way bet! Our conclusion is the same as made by Gentry and Hubbard “models [either neo- classical or Austrian] emphasizing a link between entrepreneurial talent [un- derstood in the Austrian tradition as entrepreneurial alertness] and selection into entrepreneurship predict a negative correlation between increases in tax progressivity and entrepreneurial entry probabilities” (2000, p. 284). Our analysis also answers the question posed by Gentry and Hubbard, 2000, p. 282 (and they were unable to answer and left for future research), “when tax rates are less progressive and hence there is encouragement of entrepreneur- ial entry is this efficient, that is stimulating the most talented entrepreneurs.” In other words, “to what extend do progressive marginal tax rates discourage entry by entrepreneurs with the most promising business projects?” (o.c. p. 287). From the Austrian point of view, to correct an error is, as just-said, a one way bet. To ask the question if this is efficient, is to deny the benign qual- ity of the market system: the correction of fundamental errors. To conclude, by taxing pure profit, the discovery process is seriously ham- pered. By lowering profits (especially since risk is at hand), impeding on the first one -that is the entrepreneur- in the discovery process, and changing by a central government relative preferences with unknown consequences, dis- 28 Auke R. Leen covery is seriously harmed. If there should be taxation, taxing consumers without changing relative prices seems to be the least intrusive way to collect taxes in the competitive-entrepreneurial discovery process of the market.
NOTES
1. In this paper I do not give ‘the’ but ‘an’ Austrian approach to taxation. As far as there are other (non- and Austrian) approaches, there is of course the partial equilibrium approach of the Marshallians: we do only look at a par- ticular tax in isolation and then analyze it effects. Next we do have the Wal- rasian (general equilibrium) and Keynesian approach: we do look not on- ly at what the government takes out of the economy but at what it spends too. In other words, we look at the whole budgetary process of tax-and- spend. As far as the Austrians go, for Mises, the founder of modern-Aus- trian economics, first, taxation is a matter of the market economy. Under socialism “the government no longer depends for its financial support on the means extracted from the citizen” (1966, p. 740). Second, since the role of the government in a fully-fledged market economy is very small, taxes “are low and do not perceptible disarrange production and consumption” (o.c., p. 740). In general, also, though taxes are a phenomenon of the mar- ket economy they do not have to bother us in a perfect (Austrian) market economy. The small amount of it, per se, does make it unimportant. 2. The situation is even worse. We do have an almost confiscatory taxa- tion of potentially successful endeavors and, in fact, a tax subsidy for safe, nonentrepreneurial undertakings. “[P]eople do not like insecure loans to new businesses based on great new ideas. They do like lending secured to readily marketable assets by mortgages or similar arrange- ments” (Hall, 1996, p. 32). Uncertainty, taxation and entrepreneurial entry 29
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CONFIDENCE INTERVALS IN STATIONARY AUTOCORRELATED TIME SERIES
G.E. HALKOS I.S. KEVORK
University of Thessaly University of Thessaly
Abstract
George E. Halkos - Ilias S. Kevork: Confidence intervals in stationary autocorrelated time series. In this study we examine in covariance stationary time series the consequences of con- structing confidence intervals for the population mean using the classical methodology based on the hypothesis of independence. As criteria we use the actual probability the con- fidence interval of the classical methodology to include the population mean (actual confi- dence level), and the ratio of the sampling error of the classical methodology over the cor- responding actual one leading to equality between actual and nominal confidence levels. These criteria are computed analytically under different sample sizes, and for different au- tocorrelation structures. For the AR(1) case, we find significant differentiation in the val- ues taken by the two criteria depending upon the structure and the degree of autocorrela- tion. In the case of MA(1), and especially for positive autocorrelation, we always find ac- tual confidence levels lower than the corresponding nominal ones, while this differentiation between these two levels is much lower compared to the case of AR(1). JEL: C5. Keywords: Covariance stationaty time series, Variance of the sample mean, Actual con- fidence level.
1. Introduction
The basic assumption required at the stage of constructing confidence in- tervals for the mean, Ì, of normally distributed populations is the observa- tions in the sample to be independent. In a number of cases, however, the 32 G. E. Halkos - I.S. Kevork validity of this assumption should be seriously taken under consideration, and as a representative example we mention the problem of constructing confidence intervals for the average delay of customers in queuing systems. In such a case, it is very common the delays in a sample of n successive cus- tomers to display a certain degree of dependency at different lags, and therefore the application of the classical confidence interval estimator for the steady-state mean, Ì, Û Û Ã Z ≤ Ì ≤ X ∑ (1) ·/2 n ·/2 n based on independent, identical, and normal random variables not to be recommended.
Fishman (1978) shows that the variance of the mean of a sample X1, X2, … , Xn from a covariance stationary process is: Û2 Var(X ) x h(p ) (2) n n s with n 1 s h(ps) 1 2 1 ps (3) s 1 n th and ps to be the s lag theoretical autocorrelation coefficient between any two variables whose time distance is s. Covariance stationary means that the mean and variance of {Xt, t = 1, 2, …} are stationary over time 2 with common finite mean Ì and common finite variance Ûx. Moreover for a covariance stationary process, the covariance between Xt and Xt+s de- pends only on the lag s and not on their actual values at times t and t+s. For the last two decades, alternative estimators for (2) have been proposed in the literature in the context of estimating steady-state means in stationary simulation outputs. The reason for developing such variance estimators and not using directly the estimated values of the autocorrelation coefficients in
(2) is that, for s close to n, the estimation of ps (s = 1, 2 ,…, n - 1) will be not accurate as it will be based on few observations. On the other hand, Kevork (1990) showed that fixed sample size variance estimators, based on a single long replication, have two serious disadvantages. First, in finite samples they are biased. Second, the recommended values for their parameters at the esti- mation stage differ significantly according to the structure and the degree of the autocorrelation, which characterizes the process under consideration. Confidence intervals in stationary autocorrelated time series 33
Taking these two disadvantages into consideration at this stage, we are asked ourselves in what extent the application of these complicated vari- ance estimators of (2) is necessary for covariance stationary processes. In other words can we avoid their use by investigating the consequences of ap- plying the simple confidence interval estimator (1) to covariance station- ary processes so that after making appropriate modifications to improve its performance? Answers to the above questions are given in the current study. More specifically, assuming that the process under consideration follows either the first order autoregressive model, AR(1), or the first order moving average model, MA(1), we investigate the consequences of using (1) for estimating the steady-state mean in the light of the following two criteria: a) the differ- ence between the nominal confidence level and the corresponding actual confidence level which is attained by (1); and b) the ratio of the sampling er- ror of (1) over the corresponding real sampling error which ensures equali- ty among nominal and actual confidence levels. These two criteria are com- puted analytically for the AR(1) and MA(1) under different values of the pa- rameters Ê and ı respectively, and for different sample sizes. The results for the AR(1) verify that the use of the complicated variance estimators for (2) is inevitable, especially when Ê is positive and less than one. On the other hand, for the MA(1) the difference between a nominal confidence level of 95% and the achieved actual one is predictable as in low positive autocor- relations it ranges at 5%, while for moderate and high autocorrelations the difference remains almost constant with an average of 10%. Under the above considerations, the structure of the paper is as follows: In section 2 we review the existing literature concerning the available variance estimators for (2). In section 3, we derive analytic forms for the special func- tion of autocorrelation coefficients, h(ps), for AR(1) and MA(1). In the same section we specify the conditions when this function takes positive values less or greater than one. In section 4, we establish the methodology for com- puting analytically the actual confidence levels attained by using (1), that is, the actual probability this interval to include the real steady-state mean of the covariance stationary process. Additionally, we present the actual con- fidence levels that (1) achieves in AR(1) and MA(1), for different degrees of autocorrelation under different sample sizes. Finally, the last section pres- ents the main findings and conclusions of this research. 34 G. E. Halkos - I.S. Kevork
2. Literature review
The presence of autocorrelation in simulation output may be a chal- lenge for Inferential Statistics. This is because the lack of independence in the data becomes a serious problem and the calculation of elementary statistical measures like the standard error of the sample mean is incor- rect. In particular, when time series data are positively autocorrelated the use of the classical standard error of the sample mean creates bias- es, which as a consequence reduces the coverage probabilities of confi- dence intervals. Looking at the existing literature we may find different methods to over- come the problems of autocorrelation in the construction of confidence in- tervals for steady-state means. These methods are classified as, sequential, truncation and fixed sample size. Sequential confidence interval methods have as objective to determine the run length (sample size) of realizations of stationary simulation output processes which guarantees both an ade- quate correspondence between actual and nominal confidence levels and a pre-specified absolute or relative precision, as these terms are defined by Law (1983). Law and Kelton (1982a) distinguish these methods as regener- ative and non-regenerative. Fishman’s (1977) and Lavenberg and Sauer’s (1977) methods belong to regenerative category while the methods devel- oped by Mechanic and McKay (1966), Law and Carson (1978), Adam (1983) and Heidelberger and Welch (1981a) have been characterized as non-regenerative. For the truncation methods the objective is the elimination of initializa- tion bias effects on the estimation of the steady-state mean. These methods provide estimators for the time point t* (1 ≤ t* ≤ n) for which the absolute value of the difference between the expected value of the sample mean from the steady-state mean is greater than a pre-specified very small posi- tive number e for any t
th the j overlapping batch mean of size m [Xj(m)] may be defined and in this context Welsh (1987) proposed for large m and n/m the following sample m n m 1 ^2 2 mean variance estimator Û√µª [Xj (m) Ãn] . But n(n m 1) j 1 Sargent et al. (1992) claim that NOBM is preferable to OBM when we con- struct confidence intervals relying on small samples and probably equiva- lent in the case of using large samples.
Next, let us consider the standardized time series methods. If {Xt} is strictly stationary (the joint distribution of X , X , …, X is the same as t1 t2 tn the joint distribution of X X X for every t , t ,… , t and s) and t1 s, t2 s , tn s 1 2 n assuming also that this process is phi-mixing (for large s the correlation of
Xt and Xt+s becomes negligible; see Law, 1983), the standardized time se- ries methods use a functional central limit theorem to transform the sam- ple X1, X2,… , Xn into a process which is asymptotically distributed as a Brownian Bridge process. Dividing a single long replication into k>1 con- tiguous and non-overlapping batches of size m, for m large and by using Brownian Bridge properties, Schruben (1983) derived four methods for es- timating the variance of the sample mean. The area method, the maximum method, the combined area non-overlapping batch means method and the combined maximum non-overlapping batch means method. The standard- ized time series methods are easy to use and asymptotically have advan- tages over NOBM, but require long runs. In these lines and as a parametric time series modeling of simulation out- put data, we consider the autoregressive method of Fishman (1978). This method assumes that {Xt} is covariance stationary and can be represented by a pth order autoregressive process, AR(p). Voss et al. (1996) derived good estimates of the steady state average queue delay using data from the transient phase of the simulation using a high-order AR(p) model. But such an autoregressive method is improper for widespread use as general ARI- MA models are complex and assumptions for ARIMA modeling may be in- valid for some particular simulation models. The regenerative method was developed for the case in which the simulat- ed process is characterized by the regenerative property and by enough re- generation cycles. This method was developed by Crane and Iglehart (1974a,b,c; 1975). Its principle is based on the identification of random points, where the process probabilistically starts over again. These points Confidence intervals in stationary autocorrelated time series 37 are called regeneration points. For instance, studying the delay in queue in the M/M/1 model, the indices of customers who find the system empty can be considered as regeneration points. The amount of data between two re- generation points is called the regeneration cycle. Then, the regeneration points are used to obtain independent random variables to which inferential methods can be applied. In this context, two methods have been developed for estimating the steady state mean and producing confidence intervals, the classical and the Jacknife. A very good description of these methods is pro- vided in Law and Kelton (1982b). It is worth mentioning here that the main disadvantage of these methods is the identification of regeneration points, especially for complicated simulation models. Specifically, the problem with this method exists when either there are no regeneration points for the out- put process or when the simulation cannot produce enough cycles. A new and more recent approach to simulation output analysis relies on resampling methods, such as the Jackknife and the Bootstrap (Quenouille, 1949; Tuckey, 1958; Efron, 1979; Efron and Tibshirani, 1993), which pro- vide non-parametric estimates of bias and standard error. The Bootstrap method relies on pseudo-data created by re-sampling the actual data, but it requires independency, which is not always the case in simulation outputs. The application of this method to time series data may work by re-sampling sets of consecutive observations in order to capture the autocorrelation structure. Various forms of the Bootstrap method appear in the literature. First, the Moving Blocks Bootstrap (MBB), which relies on random re- sampling of fixed size overlapping blocks with replacement (Künsch, 1989; Liu and Singh, 1992; Hall et al., 1995). However, this method requires sub- jective inputs from the researcher and its estimates vary considerably. Second, for stationary time series the Stationary Bootstrap (SB) was de- veloped, where the data are re-sampled by contaminated blocks, which have a randomly chosen starting point and with their length geometrically distributed according to some chosen mean (Politis and Romano,1994). Un- der the same principle, Kim et al. (1993a) developed the Binary Bootstrap (BB) to analyze autocorrelated binary data. Kim et al. (1993b) introduced the Threshold Bootstrap (TB) extending the BB, and Park and Willemain (1999) modified the TB introducing the Threshold Jackknife (TJ). They claim that for various ARMA models, the TB has a better performance compared to MBB and SB in terms of estimating the standard error of the 38 G. E. Halkos - I.S. Kevork sample mean, if we optimize each re-sampling scheme with respect to the size of the re-sampling unit. They also show that the MBB has generally a poor performance. Park et al. (2001) test the TB as a non-parametric method of output analysis and show that the TB is an effective alternative to the batch means and relatively easy. They also show that the TB is more effective in the con- struction of confidence intervals for the steady state mean and median de- lay in the M/M/1 model, and establish the asymptotic unbiasedness and consistency of the TB estimators when we refer to the sample mean. Finally, we have the spectral method where the process {Xt} is assumed to be covariance stationary. At zero frequency, the power spectrum f(0) is estimated either by using the Tukey spectral window (Fishman (1973 a,b; Duket and Pritsker, 1978; Law and Kelton, 1984) or by using the peri- odogram coordinates as presented in Heidelberger and Welch (1981a,b).
3. The function h(ps) in AR(1) and MA(1) 3.1 AR(1) This model is defined by Xt ÊXt 1 Ât, and is stationary when Ê 1. The Âtãs are uncorrelated and normal random variables with mean zero and 2 th common variance ÛÂ. Substituting the s theoretical autocorrelation coeffi- s cient of this model, ps Ê , to (3) we take: n 1 1 n 1 s s h(ps) 1 2 Ê sÊ (4) s 1 n s 1 Given n 1 1 Ên 1 Ês Ê s 1 1 Ê and n 1 Ê(1 Ên) nÊn(1 Ê) s Ê 2 s 1 (1 Ê) the function h(ps) takes for the AR(1) the form: Ê Ê(1 Ên) 1 Ê 2Ê(1 Ên) h(p ) 1 2 (5) s 1 Ê n(1 Ê)2 1 Ê n(1 Ê)2 Confidence intervals in stationary autocorrelated time series 39
Subtracting 1 from both sides of (5): 2Ê h(Ú ) 1 {1 „(n, Ê)} s 1 Ê where 1 Ên „(n, Ê) n(1 Ê) Given Ê 1, for any n ≥ 2, „ (n, Ê) takes always values in the inter- val (0,1), and this is illustrated in figures 1a, 1b, and 1c. Especially, when 0.50 < Ê < 1, „ (n, Ê) converges exponentially to zero. On the contrary, for –1 < Ê < 0.50, when n is small „ (n, Ê) displays some oscillation which is getting larger and larger as Ê approaches –1, while for n large this oscil- lation vanishes and the function converges again exponentially to zero. The behaviour of „ (n, Ê) leads us to the conclusion that when Ê is positive, namely, the autocorrelation function converges exponentially to zero taking only positive values (positive autocorrelation), for any n, the function h(ps) takes values always greater than 1. This means that using the classical confidence interval estimator (1) we underestimate the real sampling error that the interval should have, and as a result we attain actual confidence levels lower that the corresponding nominal ones. On the other hand for –1 < Ê < 0, that is, the autocorrelation function converges to zero oscillating between negative and positive values (negative autocorrelation), Figure 1·: „(n, Ê) for 0 Ê 1.
1 0.9 0.8
0.7 φ=0.20 0.6 φ=0.50 0.5 φ=0.80 0.4 0.3 φ=0.90 0.2 0.1 0 0 5 101520253035 n 40 G. E. Halkos - I.S. Kevork
Figure 1b: „(n, Ê) for 0.50 ≤ Ê 0
0.45 0.4
0.35 0.3
0.25 φ=-0.20
0.2 φ=-0.50 0.15 0.1
0.05 0
0 5 10 15 20 25 30 n
Figure 1c: „(n, Ê) for 1 Ê 0.50.
0.35
0.3
0.25
0.2 φ=-0.60
0.15 φ=-0.90
0.1
0.05
0 0 5 101520253035 n for n ≥ 2 the half width of the classical estimator (1) overestimates the real sampling error, and this results in actual confidence levels greater than the corresponding nominal ones. The size of overestimating (or underestimating) the real sampling error by using (1), which is equal to 0,5 [h(ps)] , is displayed for different n and Ê in table 1. When n is large (e.g. n > 50), for the case of positive autocorrelation, the half width of the classical estimator (1) is at least 4 times narrower than the real sampling error, whereas for negative autocorrelation the real sampling error is overestimated approximately 3 times. Confidence intervals in stationary autocorrelated time series 41
Table 1: Overestimating or underestimating the real sampling error in AR(1). n Ê = -0.80 Ê = -0.50 Ê = -0.20 Ê = 0.20 Ê = 0.50 Ê = 0.80 Ê = 0.90 2 2.24 1.41 1.12 0.91 0.82 0.75 0.73 3 1.67 1.41 1.15 0.88 0.74 0.63 0.60 4 2.33 1.51 1.17 0.86 0.70 0.57 0.53 5 2.03 1.53 1.18 0.85 0.67 0.53 0.48 6 2.41 1.57 1.18 0.85 0.65 0.50 0.45 7 2.26 1.59 1.19 0.84 0.64 0.47 0.42 8 2.48 1.60 1.19 0.84 0.63 0.45 0.40 9 2.40 1.62 1.20 0.84 0.63 0.44 0.38 10 2.54 1.63 1.20 0.83 0.62 0.43 0.37 11 2.50 1.64 1.20 0.83 0.62 0.42 0.36 12 2.59 1.64 1.20 0.83 0.61 0.41 0.35 13 2.57 1.65 1.21 0.83 0.61 0.41 0.34 14 2.63 1.66 1.21 0.83 0.61 0.40 0.33 15 2.62 1.66 1.21 0.83 0.60 0.39 0.32 16 2.66 1.66 1.21 0.83 0.60 0.39 0.32 17 2.66 1.67 1.21 0.83 0.60 0.39 0.31 18 2.69 1.67 1.21 0.83 0.60 0.38 0.31 19 2.70 1.67 1.21 0.83 0.60 0.38 0.30 20 2.72 1.68 1.21 0.83 0.60 0.38 0.30 50 2.87 1.71 1.22 0.82 0.59 0.35 0.25 100 2.94 1.72 1.22 0.82 0.58 0.34 0.24 200 2.97 1.73 1.22 0.82 0.58 0.34 0.24 500 2.99 1.73 1.22 0.82 0.58 0.33 0.23
3.2 ª∞(1) It is given by Xt Ât ıÂt 1, and although the model is stationary for any ı, the invertibility condition restricts ı in the interval (-1, 1). Substi- tuting the autocorrelation function: 42 G. E. Halkos - I.S. Kevork
ı 2 p 1 ı ,s 1 s 0, s 1 into (2) we take: n 1 ı h(p ) 1 2 (6) s n 1 ı2
It is obvious that when ı is positive (negative), the function h(ps) takes values greater (positive and smaller) than one. So, as in the case of AR(1), under a positive (negative) autocorrelation the real sampling error is un- derestimated (overestimated) by using (3), attaining actual confidence lev- els lower (greater) than the nominal ones. Table 2, similar to table 1, illus- trates for positive and negative autocorrelations the size of underestimat- ing and overestimating respectively the real sampling error when we use the classical confidence interval estimator. Comparing the two tables we observe that the size of underestimation is smaller in MA(1) under positive autocorrelation especially in large samples, but for negative autocorrela- tion, the real sampling error is much more overestimated in MA(1) com- pared with the AR(1).
4. Actual confidence levels attained by the classical interval estimator in AR(1) and MA(1)
Given that the random variables X1, X2, …, Xn from a covariance sta- tionary process are normally distributed with steady-state mean Ì and common standard deviation ÛÃ, the actual confidence interval for Ì is de- rived from: Ã Ì ≤≤ Pr z· /2 z· /2 1 ·¡ ¡ Û ¡ Ã 1/2 [h(ps)] n as ÛÃ ÛÃ Ã z [h(p )]1/2 ≤ Ì ≤ Ã z [h(p )]1/2 ·¡/2 n s ·¡/2 n s Confidence intervals in stationary autocorrelated time series 43